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Algebraic Structure of Pseudocompact Groups
Dikran Dikranjan, University of Udine, Italy, and Dmitri Shakhmatov, Ehime University, Matsuyama, Japan

Memoirs of the American Mathematical Society
1998; 83 pp; softcover
Volume: 133
ISBN-10: 0-8218-0629-7
ISBN-13: 978-0-8218-0629-6
List Price: US$48
Individual Members: US$28.80
Institutional Members: US$38.40
Order Code: MEMO/133/633
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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.

Table of Contents

  • Introduction
  • Principal results
  • Preliminaries
  • Some algebraic and set-theoretic properties of pseudocompact groups
  • Three technical lemmas
  • Pseudocompact group topologies on \(\mathcal V\)-free groups
  • Pseudocompact topologies on torsion Abelian groups
  • Pseudocompact connected group topologies on Abelian groups
  • Pseudocompact topologizations versus compact ones
  • Some diagrams and open questions
  • Diagram 2
  • Diagram 3
  • Bibliography
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