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Algebraic Structure of Pseudocompact Groups
 
Dikran Dikranjan University of Udine, Udine, Italy
Dmitri Shakhmatov Ehime University, Matsuyama, Japan
Front Cover for Algebraic Structure of Pseudocompact Groups
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
Front Cover for Algebraic Structure of Pseudocompact Groups
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  • Front Cover for Algebraic Structure of Pseudocompact Groups
  • Back Cover for Algebraic Structure of Pseudocompact Groups
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.

    Readership

    Graduate 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 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.

Readership

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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