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arXiv · 1909.03607

Countably compact group topologies on the free Abelian group of size continuum (and a Wallace semigroup) from a selective ultrafilter

A. C. Boero·I. Castro-Pereira·A. H. Tomita
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Abstract

We prove that the existence of a selective ultrafilter implies the existence of a countably compact Hausdorff group topology on the free Abelian group of size continuum. As a consequence, we show that the existence of a selective ultrafilter implies the existence of a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group).

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A. C. Boero, I. Castro-Pereira, A. H. Tomita. 2019-09-09. Countably compact group topologies on the free Abelian group of size continuum (and a Wallace semigroup) from a selective ultrafilter. https://doi.org/10.1007/s10474-019-00991-w

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