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Author : Richard Eugene McGill
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.3/5 (91 download)
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:
Author : Richard Eugene McGill
Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (15 download)
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 1959 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert A. McCoy
Publisher : Springer
ISBN 13 : 3540391819
Total Pages : 128 pages
Book Rating : 4.5/5 (43 download)
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.
Author : G.L.M. Groenewegen
Publisher : Springer
ISBN 13 : 9462392013
Total Pages : 183 pages
Book Rating : 4.4/5 (623 download)
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 183 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.
Author : Jürgen Flachsmeyer
Publisher :
ISBN 13 :
Total Pages : 290 pages
Book Rating : 4.:/5 (43 download)
Download or read book Contributions to Extension Theory of Topological Structures written by Jürgen Flachsmeyer and published by . This book was released on 1969 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gerhard Preuß
Publisher : Springer Science & Business Media
ISBN 13 : 9401004897
Total Pages : 306 pages
Book Rating : 4.4/5 (1 download)
Download or read book Foundations of Topology written by Gerhard Preuß and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new foundation of Topology, summarized under the name Convenient Topology, is considered such that several deficiencies of topological and uniform spaces are remedied. This does not mean that these spaces are superfluous. It means exactly that a better framework for handling problems of a topological nature is used. In this setting semiuniform convergence spaces play an essential role. They include not only convergence structures such as topological structures and limit space structures, but also uniform convergence structures such as uniform structures and uniform limit space structures, and they are suitable for studying continuity, Cauchy continuity and uniform continuity as well as convergence structures in function spaces, e.g. simple convergence, continuous convergence and uniform convergence. Various interesting results are presented which cannot be obtained by using topological or uniform spaces in the usual context. The text is self-contained with the exception of the last chapter, where the intuitive concept of nearness is incorporated in Convenient Topology (there exist already excellent expositions on nearness spaces).
Author : Wolfgang J. Thron
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.F/5 ( download)
Download or read book Topological Structures written by Wolfgang J. Thron and published by . This book was released on 1966 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert A. McCoy
Publisher : Springer
ISBN 13 : 3319770543
Total Pages : 121 pages
Book Rating : 4.3/5 (197 download)
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 121 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.
Author : Leonard Gillman
Publisher : Courier Dover Publications
ISBN 13 : 0486816885
Total Pages : 321 pages
Book Rating : 4.4/5 (868 download)
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.
Author : Peter W. Michor
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.3/5 (91 download)
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:
Author : Gerhard Preuß
Publisher : Springer Science & Business Media
ISBN 13 : 9400928599
Total Pages : 316 pages
Book Rating : 4.4/5 (9 download)
Download or read book Theory of Topological Structures written by Gerhard Preuß and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author : Somashekhar A. Naimpally
Publisher : World Scientific
ISBN 13 : 9814407666
Total Pages : 294 pages
Book Rating : 4.8/5 (144 download)
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.
Author : Robert A. McCoy
Publisher :
ISBN 13 : 9783662169346
Total Pages : 138 pages
Book Rating : 4.1/5 (693 download)
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:
Author : A. V. Arkhangelʹskiĭ
Publisher : atlantis press
ISBN 13 : 9078677066
Total Pages : 797 pages
Book Rating : 4.0/5 (786 download)
Download or read book Topological Groups and Related Structures written by A. V. Arkhangelʹskiĭ and published by atlantis press. This book was released on 2008 with total page 797 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, the objects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groups and semigroups, paratopological groups, etc. Special emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of the operation. The main scope of the book, however, is outside of the locally compact structures, thus distinguishing the monograph from a series of more traditional textbooks.The book is unique in that it presents very important material, dispersed in hundreds of research articles, not covered by any monograph in existence. The reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the way to the frontier of the knowledge is quite short -- almost every section of the book contains several intriguing open problems whose solutions can contribute significantly to the area.
Author : Charles J. Mozzochi
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.:/5 (43 download)
Download or read book Symmetric Generalized Topological Structures written by Charles J. Mozzochi and published by . This book was released on 1976 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Hrušák
Publisher : Springer
ISBN 13 : 3319916807
Total Pages : 309 pages
Book Rating : 4.3/5 (199 download)
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 309 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.
Author : Will Chambers
Publisher : Scientific e-Resources
ISBN 13 : 1839473363
Total Pages : 284 pages
Book Rating : 4.8/5 (394 download)
Download or read book Topology written by Will Chambers and published by Scientific e-Resources. This book was released on 2018-11-22 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure. This book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject. The viewpoint is quite classical in spirit, and stays well within the confines of pure algebraic topology. Topology developed as a field of study out of geometry and set theory, through analysis of concepts such as space, dimension, and transformation. Such ideas go back to Gottfried Leibniz, who in the 17th century envisioned the geometria situs and analysis situs. Leonhard Euler's Seven Bridges of Koenigsberg Problem and Polyhedron Formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. By the middle of the 20th century, topology had become a major branch of mathematics. The motivating insight behind topology is that some geometric problems depend not on the exact shape of the objects involved, but rather on the way they are put together. For example, the square and the circle have many properties in common: they are both one dimensional objects (from a topological point of view) and both separate the plane into two parts, the part inside and the part outside.
