A Cp-Theory Problem Book : Compactness in Function Spaces / by Vladimir V. Tkachuk.

Format:

Book

Author/Creator:

Tkachuk, Vladimir V., Author.

Series:

Problem Books in Mathematics, 0941-3502

Language:

English

Subjects (All):

Algebraic topology.

Functional analysis.

Algebraic Topology.

Functional Analysis.

Local Subjects:

Algebraic Topology.

Functional Analysis.

Physical Description:

1 online resource (XV, 524 p.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

Language Note:

English

Summary:

This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level. The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. The second volume, Special Features of Function Spaces © 2014, continued from the first, giving reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. This third volume is self-contained and works in tandem with the other two, containing five hundred carefully selected problems and solutions. It can also be considered as an introduction to advanced set theory and descriptive set theory, presenting diverse topics of the theory of function spaces with the topology of point wise convergence, or Cp-theory which exists at the intersection of topological algebra, functional analysis and general topology.

Contents:

Preface

Contents

Detailed summary of exercise sections

Introduction

1. Behavior of Compactness in Function Spaces

2. Solutions of Problems 001-0500

3. Bonus Results: Some Hidden Statements

4. Open Problems

Bibliography

List of Special Symbols

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-16092-3

OCLC:

910963819