Function Spaces with Uniform, Fine and Graph Topologies. 1st ed. 2018

種類:

電子ブック

責任表示:

by Robert A. McCoy, Subiman Kundu, Varun Jindal

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• McCoy, Robert A.
• Kundu, Subiman.
• Jindal, Varun.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematics ;

ISBN:

9783319770543 [3319770543]    

注記:

Preface -- Introduction -- 1 Preliminaries -- 2 Metrizability and Completeness Properties of Cτ (X, Y ) for τ = d, f, g -- 3 Cardinal Functions and Countability Properties -- 4 Connectedness and Path Connectedness of Cτ (X, Y ) for a Normed Linear Space Y , where τ = d, f, g. - 5 Compactness in Cτ (X, Y ) for τ = d, f, g. - 6 Spaces of Homeomorphisms -- Bibliography -- List of Symbols -- Index.
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.

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