Algebraic Structure of Pseudocompact Groups by Dikran N. Dikranjan (PDF)

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    Ebook Info

    • Published:
    • Number of pages: 83 pages
    • Format: PDF
    • File Size: 8.16 MB
    • Authors: Dikran N. Dikranjan

    Description

    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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