On the Ultrafilter Semigroup of an Abelian Topological Group |
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Authors: | Yevhen Zelenyuk |
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Institution: | (1) School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa |
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Abstract: | The ultrafilter semigroup of a topological group G, denoted Ult(G), consists of all nonprincipal ultrafilters on G converging
to the identity and is a closed subsemigroup in the Stone-Cech compactification β Gd of G as a discrete semigroup. We show that for every countable nondiscrete Abelian topological group G not containing an
open Boolean subgroup, the structural group of the smallest ideal of Ult(G) has cardinality 2c. |
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Keywords: | |
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