Comfort's question on powers in $\mathbb Q ^{(2^\mathfrak c)}$ and a Wallace semigroup whose cube is countably compact

J. L. J. Fuentes-Maguiña; A. H. Tomita

Comfort's question on powers in $\mathbb Q ^{(2^\mathfrak c)}$ and a Wallace semigroup whose cube is countably compact

General Topology 2022-10-19 v2

Authors: J. L. J. Fuentes-Maguiña , A. H. Tomita

Abstract

We prove that the existence of $\mathfrak{c}$ incomparable selective ultrafilters implies the existence of a Wallace semigroup whose cube is countably compact. In addition, assuming the existence of $2^{\mathfrak c}$ incomparable selective ultrafilters and $2^{< 2^{\mathfrak{c}}} = 2^{\mathfrak{c}}$ , we obtain torsion-free topological groups with respect to Comfort's question on the countable compactness of (infinite) powers of a topological group.

Keywords

ultrafilter

Cite

@article{arxiv.2210.08688,
  title  = {Comfort's question on powers in $\mathbb Q ^{(2^\mathfrak c)}$ and a Wallace semigroup whose cube is countably compact},
  author = {J. L. J. Fuentes-Maguiña and A. H. Tomita},
  journal= {arXiv preprint arXiv:2210.08688},
  year   = {2022}
}

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23 pages

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