The product of Lindel\"of groups and $\mathbb R$-factorizability

Evgeny Reznichenko

The product of Lindel\"of groups and $\mathbb R$-factorizability

Group Theory 2023-10-03 v4 General Topology

Authors: Evgeny Reznichenko

Abstract

Lindel\"of topological groups $G_1$ , $H_1$ , $G_2$ , $H_2$ are constructed in such a way that the products of $G_1 \times H_1$ and $G_2 \times H_2$ are not $\mathbb R$ -factorizable groups and (1) the group $G_1 \times H_1$ is not pseudo- $\aleph_1$ -compact; (2) the group $G_2 \times H_2$ is a separable not normal group and contains a discrete closed subset of the cardinality continuum.

Keywords

lindelöf groups topological groups r-factorizability pseudo-aleph1-compactness separable non-normal group discrete closed subset

Cite

@article{arxiv.2303.06369,
  title  = {The product of Lindel\"of groups and $\mathbb R$-factorizability},
  author = {Evgeny Reznichenko},
  journal= {arXiv preprint arXiv:2303.06369},
  year   = {2023}
}

The product of Lindel\"of groups and $\mathbb R$-factorizability

Abstract

Keywords

Cite

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