Convergence Structures and Applications to Functional Analysis / Edition 1

by R. Beattie, Heinz-Peter Butzmann

Overview

This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional analysis, there are none with this particular focus.

The book demonstrates the applicability of convergence structures to functional analysis. Highlighted here is the role of continuous convergence, a convergence structure particularly appropriate to function spaces. It is shown to provide an excellent dual structure for both topological groups and topological vector spaces.

Readers will find the text rich in examples. Of interest, as well, are the many filter and ultrafilter proofs which often provide a fresh perspective on a well-known result.

Audience: This text will be of interest to researchers in functional analysis, analysis and topology as well as anyone already working with convergence spaces. It is appropriate for senior undergraduate or graduate level students with some background in analysis and topology.

Product Details

ISBN-13:	9789048159949
Publisher:	Springer Netherlands
Publication date:	12/09/2010
Edition description:	Softcover reprint of hardcover 1st ed. 2002
Pages:	264
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1 Convergence spaces.- 2 Uniform convergence spaces.- 3 Convergence vector spaces.- 4 Duality.- 5 Hahn-Banach extension theorems.- 6 The closed graph theorem.- 7 The Banach-Steinhaus theorem.- 8 Duality theory for convergence groups.- List of Notations.