| eBook ISBN: | 978-1-4704-0222-8 |
| Product Code: | MEMO/133/633.E |
| List Price: | $48.00 |
| MAA Member Price: | $43.20 |
| AMS Member Price: | $28.80 |
| eBook ISBN: | 978-1-4704-0222-8 |
| Product Code: | MEMO/133/633.E |
| List Price: | $48.00 |
| MAA Member Price: | $43.20 |
| AMS Member Price: | $28.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 133; 1998; 83 ppMSC: 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 set-theoretic topology and its applications.
This clear and self-contained 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 set-theoretic assumptions.
ReadershipGraduate students and research mathematicians working in algebra, set theory and topology.
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Table of Contents
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Chapters
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Introduction
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1. Principal results
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2. Preliminaries
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3. Some algebraic and set-theoretic properties of pseudocompact groups
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4. Three technical lemmas
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5. Pseudocompact group topologies on $\mathcal {V}$-free groups
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6. Pseudocompact topologies on torsion Abelian groups
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7. Pseudocompact connected group topologies on Abelian groups
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8. Pseudocompact topologizations versus compact ones
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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 set-theoretic topology and its applications.
This clear and self-contained 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 set-theoretic assumptions.
Graduate students and research mathematicians working in algebra, set theory and topology.
-
Chapters
-
Introduction
-
1. Principal results
-
2. Preliminaries
-
3. Some algebraic and set-theoretic 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
