Topological Properties Of Spaces Of Continuous Functions
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Topological Properties Of Spaces Of Continuous Functions
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Author : Robert A. McCoy
language : en
Publisher: Springer
Release Date : 2006-12-08
Topological Properties Of Spaces Of Continuous Functions written by Robert A. McCoy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
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.
Topological Properties Of Spaces Of Continuous Functions
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Author : Robert A. McCoy
language : en
Publisher:
Release Date : 2014-01-15
Topological Properties Of Spaces Of Continuous Functions written by Robert A. McCoy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Descriptive Topology In Selected Topics Of Functional Analysis
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Author : Jerzy Kąkol
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-30
Descriptive Topology In Selected Topics Of Functional Analysis written by Jerzy Kąkol and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-30 with Mathematics categories.
"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.
Spaces Of Continuous Functions
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Author : G.L.M. Groenewegen
language : en
Publisher: Springer
Release Date : 2016-06-17
Spaces Of Continuous Functions written by G.L.M. Groenewegen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-17 with Mathematics categories.
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.
Set Valued Mappings Selections And Topological Properties Of 2x
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Author : W. M. Fleischman
language : en
Publisher: Springer
Release Date : 2006-11-15
Set Valued Mappings Selections And Topological Properties Of 2x written by W. M. Fleischman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Rings Of Continuous Functions
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Author : Leonard Gillman
language : en
Publisher: Courier Dover Publications
Release Date : 2018-01-16
Rings Of Continuous Functions written by Leonard Gillman and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-16 with Mathematics categories.
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.
Recent Progress In Function Spaces
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Author : Giuseppe Di Maio
language : en
Publisher:
Release Date : 1998
Recent Progress In Function Spaces written by Giuseppe Di Maio and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Basic Topology 1
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Author : Avishek Adhikari
language : en
Publisher: Springer Nature
Release Date : 2022-07-04
Basic Topology 1 written by Avishek Adhikari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-04 with Mathematics categories.
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.
Function Spaces With Uniform Fine And Graph Topologies
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Author : Robert A. McCoy
language : en
Publisher: Springer
Release Date : 2018-04-21
Function Spaces With Uniform Fine And Graph Topologies written by Robert A. McCoy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-21 with Mathematics categories.
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.
Topology And Maps
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Author : T. Husain
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topology And Maps written by T. Husain and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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).