On extremally disconnected topological groups |
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Authors: | Yevhen Zelenyuk |
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Institution: | School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa |
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Abstract: | We introduce the notion of a partially selective ultrafilter and prove that (a) if G is an extremally disconnected topological group and p is a converging nonprincipal ultrafilter on G containing a countable discrete subset, then p is partially selective, and (b) the existence of a nonprincipal partially selective ultrafilter on a countable set implies the existence of a P-point in ω∗. Thus it is consistent with ZFC that there is no extremally disconnected topological group containing a countable discrete nonclosed subset. |
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Keywords: | primary 54H11 54A35 secondary 54G05 03E35 |
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