Algebraic Structure of Pseudocompact Groups (Memoirs of the American Mathematical Society No. 633)

Algebraic Structure of Pseudocompact Groups (Memoirs of the American Mathematical Society No. 633)

By: Dikran N. Dikranjan (author), Dimitri Shakhmatov (author)Paperback

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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.

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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.

Product Details

  • publication date: 15/04/1998
  • ISBN13: 9780821806296
  • Format: Paperback
  • Number Of Pages: 83
  • ID: 9780821806296
  • weight: 198
  • ISBN10: 0821806297

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