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Function Spaces with Uniform, Fine and Graph Topologies


Function Spaces with Uniform, Fine and Graph Topologies


SpringerBriefs in Mathematics

von: Robert A. McCoy, Subiman Kundu, Varun Jindal

53,49 €

Verlag: Springer
Format: PDF
Veröffentl.: 21.04.2018
ISBN/EAN: 9783319770543
Sprache: englisch

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Beschreibungen

<div></div><div>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.<br></div><div><p></p>

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.<p></p>

<br></div>
Preface.- Introduction.- 1 Preliminaries.-&nbsp;2 Metrizability and Completeness Properties of Cτ (X, Y ) for τ = d, f, g.- 3 Cardinal Functions and Countability Properties.-&nbsp;4 Connectedness and Path Connectedness of Cτ (X, Y ) for a Normed Linear&nbsp;Space Y , where τ = d, f, g. -&nbsp;5 Compactness in Cτ (X, Y ) for τ = d, f, g. - 6 Spaces of Homeomorphisms.- Bibliography.- List of Symbols.- Index.
The first research monograph to study exclusively uniform, fine and graph topologies on spaces of continuous functions Studies uniform and fine topologies on spaces of self-homeomorphisms on metric spaces Provides generalizations of known results in the theory of spaces of continuous functions

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