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

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.

• 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