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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On zero-dimensionality and the connected component of locally pseudocompact groups
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by D. Dikranjan and Gábor Lukács PDF
Proc. Amer. Math. Soc. 139 (2011), 2995-3008 Request permission

Abstract:

A topological group is locally pseudocompact if it contains a non-empty open set with pseudocompact closure. In this paper, we prove that if $G$ is a group with the property that every closed subgroup of $G$ is locally pseudocompact, then $G_0$ is dense in the component of the completion of $G$, and $G/G_0$ is zero-dimensional. We also provide examples of hereditarily disconnected pseudocompact groups with strong minimality properties of arbitrarily large dimension, and thus show that $G/G_0$ may fail to be zero-dimensional even for totally minimal pseudocompact groups.
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Additional Information
  • D. Dikranjan
  • Affiliation: Department of Mathematics and Computer Science, University of Udine, Via delle Scienze, 208 – Loc. Rizzi, 33100 Udine, Italy
  • Email: dikranja@dimi.uniud.it
  • Gábor Lukács
  • Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada
  • Email: lukacs@cc.umanitoba.ca
  • Received by editor(s): February 15, 2010
  • Received by editor(s) in revised form: May 30, 2010
  • Published electronically: March 23, 2011
  • Additional Notes: The first author acknowledges the financial aid received from SRA, grants P1-0292-0101, J1-9643-0101, and MTM2009-14409-C02-01
    The second author gratefully acknowledges the generous financial support received from NSERC and the University of Manitoba, which enabled him to do this research

  • Dedicated: Dedicated to Wis Comfort on the occasion of his 78th birthday
  • Communicated by: Alexander N. Dranishnikov
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 2995-3008
  • MSC (2010): Primary 22A05, 54D25, 54H11; Secondary 22D05, 54D05, 54D30
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10626-9
  • MathSciNet review: 2801639