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Topological Properties Of Spaces Of Continuous Functions
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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.
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 . This book was released on 2014-01-15 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spaces of Continuous Functions by : G.L.M. Groenewegen
Download or read book Spaces of Continuous Functions written by G.L.M. Groenewegen and published by Springer. This book was released on 2016-06-17 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given.Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem.The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.
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.
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.
Book Synopsis Topological Structures for a Space of Continuous Functions by : Richard Eugene McGill
Download or read book Topological Structures for a Space of Continuous Functions written by Richard Eugene McGill and published by . This book was released on 1958 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Rings of Continuous Functions by : Leonard Gillman
Download or read book Rings of Continuous Functions written by Leonard Gillman and published by Courier Dover Publications. This book was released on 2018-01-16 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as a text as well as a treatise, the first systematic account of the theory of rings of continuous functions remains the basic graduate-level book in this area. 1960 edition.
Book Synopsis Set-Valued Mappings, Selections and Topological Properties of 2x by : W. M. Fleischman
Download or read book Set-Valued Mappings, Selections and Topological Properties of 2x written by W. M. Fleischman and published by Springer. This book was released on 2006-11-15 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Recent Progress in Function Spaces by : Giuseppe Di Maio
Download or read book Recent Progress in Function Spaces written by Giuseppe Di Maio and published by . This book was released on 1998 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spaces of Vector-Valued Continuous Functions by : J. Schmets
Download or read book Spaces of Vector-Valued Continuous Functions written by J. Schmets and published by Springer. This book was released on 2006-11-15 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Basic Topology 1 by : Avishek Adhikari
Download or read book Basic Topology 1 written by Avishek Adhikari and published by Springer Nature. This book was released on 2022-07-04 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone–Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand–Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the concepts leading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.
Book Synopsis Topological Spaces by : Claude Berge
Download or read book Topological Spaces written by Claude Berge and published by Courier Corporation. This book was released on 1997-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent study of sets in topological spaces and topological vector spaces includes systematic development of the properties of multi-valued functions. Topics include families of sets, topological spaces, mappings of one set into another, ordered sets, more. Examples included from different domains. 1963 edition.
Download or read book Topology and Maps written by T. Husain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is suitable for undergraduate students as well as advanced students and research workers. It consists of ten chapters, the first six of which are meant for beginners and are therefore suitable for undergraduate students; Chapters VII-X are suitable for advanced students and research workers interested in functional analysis. This book has two special features: First, it contains generalizations of continuous maps on topological spaces, e. g. , almost continuous maps, nearly continuous maps, maps with closed graph, graphically continuous maps, w-continuous maps, and a-continuous maps, etc. and some of their properties. The treatment of these notions appears here, in Chapter VII, for the first time in book form. The second feature consists in some not-so-easily-available nuptial delights that grew out of the marriage of topology and functional analysis; they are topics mainly courted by functional analysts and seldom given in topology books. Specifically, one knows that the set C(X) of all real- or com plex-valued continuous functions on a completely regular space X forms a locally convex topological algebra, a fortiori a topological vector space, in the compact-open topology. A number of theorems are known: For example, C(X) is a Banach space iff X is compact, or C(X) is complete iff X is a kr-space, and so on. Chapters VIII and X include this material, which, to the regret of many interested readers has not previously been available in book form (a recent publication (Weir [\06]) does, however, contain some material of our Chapter X).
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.
Book Synopsis Rings of Continuous Functions by : L. Gillman
Download or read book Rings of Continuous Functions written by L. Gillman and published by . This book was released on 2014-01-15 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopedia of General Topology by : K.P. Hart
Download or read book Encyclopedia of General Topology written by K.P. Hart and published by Elsevier. This book was released on 2003-11-18 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: • More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms
Book Synopsis Recent Progress in General Topology by : M. Husek
Download or read book Recent Progress in General Topology written by M. Husek and published by Elsevier. This book was released on 1992-11-20 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan, North-Holland, 1984), which gives an almost complete picture of the state of the art of Set Theoretic Topology before 1984. In the present volume several important developments are surveyed that surfaced in the period 1984-1991. This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990). Solutions to some of the original 1100 open problems are discussed and new problems are posed.
