Electronic ISBN:  9781470402228 
Product Code:  MEMO/133/633.E 
83 pp 
List Price:  $48.00 
MAA Member Price:  $43.20 
AMS Member Price:  $28.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 133; 1998MSC: Primary 22; 54; Secondary 03; 20;
The fundamental property of compact spaces—that continuous functions defined on compact spaces are bounded—served as a motivation for E. Hewitt to introduce the notion of a pseudocompact space. The class of pseudocompact spaces proved to be of fundamental importance in settheoretic topology and its applications.
This clear and selfcontained exposition offers a comprehensive treatment of the question, When does a group admit an introduction of a pseudocompact Hausdorff topology that makes group operations continuous? Equivalently, what is the algebraic structure of a pseudocompact Hausdorff group?
The authors have adopted a unifying approach that covers all known results and leads to new ones. Results in the book are free of any additional settheoretic assumptions.ReadershipGraduate students and research mathematicians working in algebra, set theory and topology.

Table of Contents

Chapters

Introduction

1. Principal results

2. Preliminaries

3. Some algebraic and settheoretic properties of pseudocompact groups

4. Three technical lemmas

5. Pseudocompact group topologies on $\mathcal {V}$free groups

6. Pseudocompact topologies on torsion Abelian groups

7. Pseudocompact connected group topologies on Abelian groups

8. Pseudocompact topologizations versus compact ones

9. Some diagrams and open questions


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The fundamental property of compact spaces—that continuous functions defined on compact spaces are bounded—served as a motivation for E. Hewitt to introduce the notion of a pseudocompact space. The class of pseudocompact spaces proved to be of fundamental importance in settheoretic topology and its applications.
This clear and selfcontained exposition offers a comprehensive treatment of the question, When does a group admit an introduction of a pseudocompact Hausdorff topology that makes group operations continuous? Equivalently, what is the algebraic structure of a pseudocompact Hausdorff group?
The authors have adopted a unifying approach that covers all known results and leads to new ones. Results in the book are free of any additional settheoretic assumptions.
Graduate students and research mathematicians working in algebra, set theory and topology.

Chapters

Introduction

1. Principal results

2. Preliminaries

3. Some algebraic and settheoretic properties of pseudocompact groups

4. Three technical lemmas

5. Pseudocompact group topologies on $\mathcal {V}$free groups

6. Pseudocompact topologies on torsion Abelian groups

7. Pseudocompact connected group topologies on Abelian groups

8. Pseudocompact topologizations versus compact ones

9. Some diagrams and open questions