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Algebraic Structure of Pseudocompact Groups

Dikran Dikranjan University of Udine, Udine, Italy
Dmitri Shakhmatov Ehime University, Matsuyama, Japan
Available Formats:
Electronic ISBN: 978-1-4704-0222-8
Product Code: MEMO/133/633.E
83 pp
List Price: $48.00 MAA Member Price:$43.20
AMS Member Price: $28.80 Click above image for expanded view Algebraic Structure of Pseudocompact Groups Dikran Dikranjan University of Udine, Udine, Italy Dmitri Shakhmatov Ehime University, Matsuyama, Japan Available Formats:  Electronic ISBN: 978-1-4704-0222-8 Product Code: MEMO/133/633.E 83 pp  List Price:$48.00 MAA Member Price: $43.20 AMS Member Price:$28.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 1331998
MSC: 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.

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
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Volume: 1331998
MSC: 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.

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
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