Function Spaces with Uniform, Fine and Graph Topologies

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.

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

Inhalt
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.