Author: Robert A. McCoy
Publisher: Springer
ISBN: 3540391819
Category : Mathematics
Languages : en
Pages : 128
Book Description
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
Author: Robert A. McCoy
Publisher: Springer
ISBN: 3540391819
Category : Mathematics
Languages : en
Pages : 128
Book Description
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.
Publisher: Springer
ISBN: 3540391819
Category : Mathematics
Languages : en
Pages : 128
Book Description
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
Author: Robert A. McCoy
Publisher:
ISBN: 9783662169346
Category :
Languages : en
Pages : 138
Book Description
Publisher:
ISBN: 9783662169346
Category :
Languages : en
Pages : 138
Book Description
Spaces of Continuous Functions
Author: G.L.M. Groenewegen
Publisher: Springer
ISBN: 9462392013
Category : Mathematics
Languages : en
Pages : 173
Book Description
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.
Publisher: Springer
ISBN: 9462392013
Category : Mathematics
Languages : en
Pages : 173
Book Description
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.
Descriptive Topology in Selected Topics of Functional Analysis
Author: Jerzy Kąkol
Publisher: Springer Science & Business Media
ISBN: 1461405297
Category : Mathematics
Languages : en
Pages : 494
Book Description
"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.
Publisher: Springer Science & Business Media
ISBN: 1461405297
Category : Mathematics
Languages : en
Pages : 494
Book Description
"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.
Function Spaces with Uniform, Fine and Graph Topologies
Author: Robert A. McCoy
Publisher: Springer
ISBN: 3319770543
Category : Mathematics
Languages : en
Pages : 106
Book Description
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.
Publisher: Springer
ISBN: 3319770543
Category : Mathematics
Languages : en
Pages : 106
Book Description
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.
Topological Structures for a Space of Continuous Functions
Author: Richard Eugene McGill
Publisher:
ISBN:
Category : Functions, Continuous
Languages : en
Pages : 68
Book Description
Publisher:
ISBN:
Category : Functions, Continuous
Languages : en
Pages : 68
Book Description
Set-Valued Mappings, Selections and Topological Properties of 2x
Author: W. M. Fleischman
Publisher: Springer
ISBN: 3540364196
Category : Mathematics
Languages : en
Pages : 125
Book Description
Publisher: Springer
ISBN: 3540364196
Category : Mathematics
Languages : en
Pages : 125
Book Description
Rings of Continuous Functions
Author: Leonard Gillman
Publisher: Courier Dover Publications
ISBN: 0486816885
Category : Mathematics
Languages : en
Pages : 321
Book Description
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.
Publisher: Courier Dover Publications
ISBN: 0486816885
Category : Mathematics
Languages : en
Pages : 321
Book Description
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
Author: Giuseppe Di Maio
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 304
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 304
Book Description
Spaces of Vector-Valued Continuous Functions
Author: J. Schmets
Publisher: Springer
ISBN: 3540409513
Category : Mathematics
Languages : en
Pages : 124
Book Description
Publisher: Springer
ISBN: 3540409513
Category : Mathematics
Languages : en
Pages : 124
Book Description