ar X iv : 0 90 9 . 13 90 v 1 [ m at h . G N ] 8 S ep 2 00 9 On zero - dimensionality and the connected component of locally pseudocompact groups *
نویسنده
چکیده
A topological group is locally pseudocompact if it contains a non-empty open set with pseudocompact closure. In this note, we study connectedness and disconnectedness properties of groups G with the property that every closed subgroup of G is locally pseudocompact. We show that the completion of the component G0 of G contains every connected compact subgroup of the completion of G. We also prove that the question of whether G/G0 is zero-dimensional (or equivalently, whether G0 is dense in the component of the completion of G) can be reduced to the case where G is a dense subgroup of a group of the form N×R, where N is zero-dimensional and compact.
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تاریخ انتشار 2009