Topological Function Spaces

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Topological Function Spaces

Author : A.V. Arkhangel'skii
Publisher : Springer
ISBN 13 : 9780792315315
Total Pages : 205 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis Topological Function Spaces by : A.V. Arkhangel'skii

Download or read book Topological Function Spaces written by A.V. Arkhangel'skii and published by Springer. This book was released on 1991-11-30 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi, "0' si j'avait su oomment en revenir. human race. It has put common sense back je n'y serais point aile: ' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'el: re of this series.

Topological Properties of Spaces of Continuous Functions

Author : Robert A. McCoy
Publisher : Springer
ISBN 13 : 3540391819
Total Pages : 128 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Topological Properties of Spaces of Continuous Functions by : Robert A. McCoy

Download or read book Topological Properties of Spaces of Continuous Functions written by Robert A. McCoy and published by Springer. This book was released on 2006-12-08 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together into a general setting various techniques in the study of the topological properties of spaces of continuous functions. The two major classes of function space topologies studied are the set-open topologies and the uniform topologies. Where appropriate, the analogous theorems for the two major classes of topologies are studied together, so that a comparison can be made. A chapter on cardinal functions puts characterizations of a number of topological properties of function spaces into a more general setting: some of these results are new, others are generalizations of known theorems. Excercises are included at the end of each chapter, covering other kinds of function space topologies. Thus the book should be appropriate for use in a classroom setting as well as for functional analysis and general topology. The only background needed is some basic knowledge of general topology.

A Cp-Theory Problem Book

Author : Vladimir V. Tkachuk
Publisher : Springer Science & Business Media
ISBN 13 : 1441974423
Total Pages : 497 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A Cp-Theory Problem Book by : Vladimir V. Tkachuk

Download or read book A Cp-Theory Problem Book written by Vladimir V. Tkachuk and published by Springer Science & Business Media. This book was released on 2011-03-23 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of function spaces endowed with the topology of point wise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from each of these areas of research. Through over 500 carefully selected problems and exercises, this volume provides a self-contained introduction to Cp-theory and general topology. By systematically introducing each of the major topics in Cp-theory, this volume is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research. Key features include: - A unique problem-based introduction to the theory of function spaces. - Detailed solutions to each of the presented problems and exercises. - A comprehensive bibliography reflecting the state-of-the-art in modern Cp-theory. - Numerous open problems and directions for further research. This volume can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists studying Cp-theory and related topics. This book also provides numerous topics for PhD specialization as well as a large variety of material suitable for graduate research.

Topology with Applications

Author : Somashekhar A. Naimpally
Publisher : World Scientific
ISBN 13 : 9814407666
Total Pages : 294 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Topology with Applications by : Somashekhar A. Naimpally

Download or read book Topology with Applications written by Somashekhar A. Naimpally and published by World Scientific. This book was released on 2013 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.

The Infinite-Dimensional Topology of Function Spaces

Author : J. van Mill
Publisher : Elsevier
ISBN 13 : 9780080929774
Total Pages : 642 pages
Book Rating : 4.9/5 (297 download)

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Book Synopsis The Infinite-Dimensional Topology of Function Spaces by : J. van Mill

Download or read book The Infinite-Dimensional Topology of Function Spaces written by J. van Mill and published by Elsevier. This book was released on 2002-05-24 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we study function spaces of low Borel complexity. Techniques from general topology, infinite-dimensional topology, functional analysis and descriptive set theory are primarily used for the study of these spaces. The mix of methods from several disciplines makes the subject particularly interesting. Among other things, a complete and self-contained proof of the Dobrowolski-Marciszewski-Mogilski Theorem that all function spaces of low Borel complexity are topologically homeomorphic, is presented. In order to understand what is going on, a solid background in infinite-dimensional topology is needed. And for that a fair amount of knowledge of dimension theory as well as ANR theory is needed. The necessary material was partially covered in our previous book `Infinite-dimensional topology, prerequisites and introduction'. A selection of what was done there can be found here as well, but completely revised and at many places expanded with recent results. A `scenic' route has been chosen towards the Dobrowolski-Marciszewski-Mogilski Theorem, linking the results needed for its proof to interesting recent research developments in dimension theory and infinite-dimensional topology. The first five chapters of this book are intended as a text for graduate courses in topology. For a course in dimension theory, Chapters 2 and 3 and part of Chapter 1 should be covered. For a course in infinite-dimensional topology, Chapters 1, 4 and 5. In Chapter 6, which deals with function spaces, recent research results are discussed. It could also be used for a graduate course in topology but its flavor is more that of a research monograph than of a textbook; it is therefore more suitable as a text for a research seminar. The book consequently has the character of both textbook and a research monograph. In Chapters 1 through 5, unless stated otherwise, all spaces under discussion are separable and metrizable. In Chapter 6 results for more general classes of spaces are presented. In Appendix A for easy reference and some basic facts that are important in the book have been collected. The book is not intended as a basis for a course in topology; its purpose is to collect knowledge about general topology. The exercises in the book serve three purposes: 1) to test the reader's understanding of the material 2) to supply proofs of statements that are used in the text, but are not proven there 3) to provide additional information not covered by the text. Solutions to selected exercises have been included in Appendix B. These exercises are important or difficult.

Manifolds of Differentiable Mappings

Author : Peter W. Michor
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Manifolds of Differentiable Mappings by : Peter W. Michor

Download or read book Manifolds of Differentiable Mappings written by Peter W. Michor and published by . This book was released on 1980 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Function Spaces with Uniform, Fine and Graph Topologies

Author : Robert A. McCoy
Publisher : Springer
ISBN 13 : 3319770543
Total Pages : 106 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Function Spaces with Uniform, Fine and Graph Topologies by : Robert A. McCoy

Download or read book Function Spaces with Uniform, Fine and Graph Topologies written by Robert A. McCoy and published by Springer. This book was released on 2018-04-21 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing literature. The goal of this monograph is to provide an extensive study of the uniform, fine and graph topologies on the space C(X,Y) of all continuous functions from a Tychonoff space X to a metric space (Y,d); and the uniform and fine topologies on the space H(X) of all self-homeomorphisms on a metric space (X,d). The subject matter of this monograph is significant from the theoretical viewpoint, but also has applications in areas such as analysis, approximation theory and differential topology. Written in an accessible style, this book will be of interest to researchers as well as graduate students in this vibrant research area.

Descriptive Topology in Selected Topics of Functional Analysis

Author : Jerzy Kąkol
Publisher : Springer Science & Business Media
ISBN 13 : 1461405297
Total Pages : 494 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Descriptive Topology in Selected Topics of Functional Analysis by : Jerzy Kąkol

Download or read book Descriptive Topology in Selected Topics of Functional Analysis written by Jerzy Kąkol and published by Springer Science & Business Media. This book was released on 2011-08-30 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.

A Course on Topological Vector Spaces

Author : Jürgen Voigt
Publisher : Springer Nature
ISBN 13 : 3030329453
Total Pages : 152 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis A Course on Topological Vector Spaces by : Jürgen Voigt

Download or read book A Course on Topological Vector Spaces written by Jürgen Voigt and published by Springer Nature. This book was released on 2020-03-06 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory of topological vector spaces, with a focus on locally convex spaces. It discusses topologies in dual pairs, culminating in the Mackey-Arens theorem, and also examines the properties of the weak topology on Banach spaces, for instance Banach’s theorem on weak*-closed subspaces on the dual of a Banach space (alias the Krein-Smulian theorem), the Eberlein-Smulian theorem, Krein’s theorem on the closed convex hull of weakly compact sets in a Banach space, and the Dunford-Pettis theorem characterising weak compactness in L1-spaces. Lastly, it addresses topics such as the locally convex final topology, with the application to test functions D(Ω) and the space of distributions, and the Krein-Milman theorem. The book adopts an “economic” approach to interesting topics, and avoids exploring all the arising side topics. Written in a concise mathematical style, it is intended primarily for advanced graduate students with a background in elementary functional analysis, but is also useful as a reference text for established mathematicians.

Introduction to Uniform Spaces

Author : I. M. James
Publisher : Cambridge University Press
ISBN 13 : 9780521386203
Total Pages : 160 pages
Book Rating : 4.3/5 (862 download)

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Book Synopsis Introduction to Uniform Spaces by : I. M. James

Download or read book Introduction to Uniform Spaces written by I. M. James and published by Cambridge University Press. This book was released on 1990-05-03 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, much of which is published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces. Readers interested in general topology will find much to interest them here.

Introduction to Metric and Topological Spaces

Author : Wilson A Sutherland
Publisher : Oxford University Press
ISBN 13 : 0191568309
Total Pages : 219 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Introduction to Metric and Topological Spaces by : Wilson A Sutherland

Download or read book Introduction to Metric and Topological Spaces written by Wilson A Sutherland and published by Oxford University Press. This book was released on 2009-06-18 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.

Topological Spaces

Author : Gerard Buskes
Publisher : Springer Science & Business Media
ISBN 13 : 1461206650
Total Pages : 321 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Topological Spaces by : Gerard Buskes

Download or read book Topological Spaces written by Gerard Buskes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.

Infinite-Dimensional Topology

Author : J. van Mill
Publisher : Elsevier
ISBN 13 : 0080933688
Total Pages : 401 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Infinite-Dimensional Topology by : J. van Mill

Download or read book Infinite-Dimensional Topology written by J. van Mill and published by Elsevier. This book was released on 1988-12-01 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed. One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.

Algebraic Topology of Finite Topological Spaces and Applications

Author : Jonathan A. Barmak
Publisher : Springer Science & Business Media
ISBN 13 : 3642220029
Total Pages : 184 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Algebraic Topology of Finite Topological Spaces and Applications by : Jonathan A. Barmak

Download or read book Algebraic Topology of Finite Topological Spaces and Applications written by Jonathan A. Barmak and published by Springer Science & Business Media. This book was released on 2011-08-24 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.

Pseudocompact Topological Spaces

Author : Michael Hrušák
Publisher : Springer
ISBN 13 : 3319916807
Total Pages : 299 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Pseudocompact Topological Spaces by : Michael Hrušák

Download or read book Pseudocompact Topological Spaces written by Michael Hrušák and published by Springer. This book was released on 2018-07-19 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, intended for postgraduate students and researchers, presents many results of historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of pseudocompactness which generalizes a property of compact subsets of the real line. A topological space is pseudocompact if the range of any real-valued, continuous function defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures. The collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. In addition, the text examines new lines of research that have been at the forefront of mathematics. There is, as yet, no text that systematically compiles and develops the extensive theory of pseudocompact spaces, making this book an essential asset for anyone in the field of topology.

Topological Function Spaces

Author : A.V. Arkhangel'skii
Publisher : Springer
ISBN 13 : 9789401051477
Total Pages : 205 pages
Book Rating : 4.0/5 (514 download)

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Book Synopsis Topological Function Spaces by : A.V. Arkhangel'skii

Download or read book Topological Function Spaces written by A.V. Arkhangel'skii and published by Springer. This book was released on 2012-10-21 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi, "0' si j'avait su oomment en revenir. human race. It has put common sense back je n'y serais point aile:' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'el:re of this series.

Topological Vector Spaces, Distributions and Kernels

Author : François Treves
Publisher : Elsevier
ISBN 13 : 1483223620
Total Pages : 582 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Topological Vector Spaces, Distributions and Kernels by : François Treves

Download or read book Topological Vector Spaces, Distributions and Kernels written by François Treves and published by Elsevier. This book was released on 2016-06-03 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Vector Spaces, Distributions and Kernels discusses partial differential equations involving spaces of functions and space distributions. The book reviews the definitions of a vector space, of a topological space, and of the completion of a topological vector space. The text gives examples of Frechet spaces, Normable spaces, Banach spaces, or Hilbert spaces. The theory of Hilbert space is similar to finite dimensional Euclidean spaces in which they are complete and carry an inner product that can determine their properties. The text also explains the Hahn-Banach theorem, as well as the applications of the Banach-Steinhaus theorem and the Hilbert spaces. The book discusses topologies compatible with a duality, the theorem of Mackey, and reflexivity. The text describes nuclear spaces, the Kernels theorem and the nuclear operators in Hilbert spaces. Kernels and topological tensor products theory can be applied to linear partial differential equations where kernels, in this connection, as inverses (or as approximations of inverses), of differential operators. The book is suitable for vector mathematicians, for students in advanced mathematics and physics.