Topology and Maps

  • Taqdir Husain

Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 5)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Taqdir Husain
    Pages 1-19
  3. Taqdir Husain
    Pages 21-51
  4. Taqdir Husain
    Pages 53-76
  5. Taqdir Husain
    Pages 103-147
  6. Taqdir Husain
    Pages 195-236
  7. Taqdir Husain
    Pages 237-265
  8. Taqdir Husain
    Pages 267-288
  9. Taqdir Husain
    Pages 289-325
  10. Back Matter
    Pages 333-337

About this book

Introduction

This work is suitable for undergraduate students as well as advanced students and research workers. It consists of ten chapters, the first six of which are meant for beginners and are therefore suitable for undergraduate students; Chapters VII-X are suitable for advanced students and research workers interested in functional analysis. This book has two special features: First, it contains generalizations of continuous maps on topological spaces, e. g. , almost continuous maps, nearly continuous maps, maps with closed graph, graphically continuous maps, w-continuous maps, and a-continuous maps, etc. and some of their properties. The treatment of these notions appears here, in Chapter VII, for the first time in book form. The second feature consists in some not-so-easily-available nuptial delights that grew out of the marriage of topology and functional analysis; they are topics mainly courted by functional analysts and seldom given in topology books. Specifically, one knows that the set C(X) of all real- or com­ plex-valued continuous functions on a completely regular space X forms a locally convex topological algebra, a fortiori a topological vector space, in the compact-open topology. A number of theorems are known: For example, C(X) is a Banach space iff X is compact, or C(X) is complete iff X is a kr-space, and so on. Chapters VIII and X include this material, which, to the regret of many interested readers has not previously been available in book form (a recent publication (Weir [\06]) does, however, contain some material of our Chapter X).

Keywords

Baire space Banach space Compact space Compactification Separation axiom algebra boundary element method compactness functional functional analysis functions set theorem topological vector space topology

Authors and affiliations

  • Taqdir Husain
    • 1
  1. 1.McMaster UniversityHamiltonCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-8798-9
  • Copyright Information Springer-Verlag US 1977
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4615-8800-9
  • Online ISBN 978-1-4615-8798-9
  • About this book