On the Ultrafilter Semigroup of a Topological Group |
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Authors: | Yevhen Zelenyuk |
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Affiliation: | (1) School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa |
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Abstract: | The ultrafilter semigroup Ult(G) of a topological group G consists of all nonprincipal ultrafilters on G converging to the identity and is a closed subsemigroup in the Stone-Cech compactification βGd of G as a discrete semigroup. We show that it is consistent with ZFC that for every countable nondiscrete topological group G, Ult(G) can be partitioned into closed right ideals each of which admits a continuous homomorphism onto the Bohr compactification of the integers. |
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