Function Spaces with Uniform, Fine and Graph Topologies

1. Auflage 2018
ISBN: 978-3-319-77053-6
Verlag: Springer

Buch, Englisch, 106 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 203 g

Reihe: SpringerBriefs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

McCoy, Robert A.

Kundu, Subiman

Jindal, Varun

Fachgebiete

• Mathematik | Informatik Mathematik Topologie

Inhaltsverzeichnis

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