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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.
List of contents
Preface.- Introduction.- 1 Preliminaries.- 2 Metrizability and Completeness Properties of C (X, Y ) for = d, f, g.- 3 Cardinal Functions and Countability Properties.- 4 Connectedness and Path Connectedness of C (X, Y ) for a Normed Linear Space Y , where = d, f, g. - 5 Compactness in C (X, Y ) for = d, f, g. - 6 Spaces of Homeomorphisms.- Bibliography.- List of Symbols.- Index.
Summary
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.
Additional text
“The monograph provides a detailed introduction to the theory of function spaces with uniform, fine and graph topologies together with complete proofs of the most up to date results in the area. The book will certainly be useful for specialists working in topology and functional analysis as well as for students who need to learn the basics of the theory of the respective function spaces.” (Vladimir Tkachuk, zbMATH 1395.54001, 2018)
Report
"The monograph provides a detailed introduction to the theory of function spaces with uniform, fine and graph topologies together with complete proofs of the most up to date results in the area. The book will certainly be useful for specialists working in topology and functional analysis as well as for students who need to learn the basics of the theory of the respective function spaces." (Vladimir Tkachuk, zbMATH 1395.54001, 2018)
