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  • On zero-dimensionality and the connected component of locally pseudocompact groups
    Dikranjan, Dikran N., 1950- ; Lukács, Gábor, 1982-
    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 is ▫$G/G_0$▫ 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.
    Source: Proceedings of the American Mathematical Society. - ISSN 0002-9939 (Vol. 139, no. 8, 2011, str. 2995-3008)
    Type of material - article, component part
    Publish date - 2011
    Language - english
    COBISS.SI-ID - 15949145

    Link(s):

    http://dx.doi.org/10.1090/S0002-9939-2011-10626-9

source: Proceedings of the American Mathematical Society. - ISSN 0002-9939 (Vol. 139, no. 8, 2011, str. 2995-3008)

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