Algebraic Structure of Pseudocompact Groups

Buch | Softcover

1998
American Mathematical Society (Verlag)
9780821806296 (ISBN)

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Introduces the notion of a pseudocompact space. This work offers a comprehensive treatment of the question - When does a group admit an introduction of a pseudocompact Hausdorff topology that makes group operations continuous?

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.

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.

Erscheint lt. Verlag	30.4.1998
Reihe/Serie	Memoirs of the American Mathematical Society
Zusatzinfo	bibliography
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-13	9780821806296 / 9780821806296
Zustand	Neuware