Metrizability of CHART groups

Evgenii Reznichenko

doi:10.1016/j.topol.2023.108408

paper

Metrizability of CHART groups

arXiv:2210.01631 · doi:10.1016/j.topol.2023.108408

Abstract

For compact Hausdorff admissible right topological (CHART) group $G$ , we prove $w (G) = π χ (G)$ . This equality is well known for compact topological groups. This implies the criteria for the metrizability of CHART groups: if $G$ is first-countable (2013, Moors, Namioka) or $G$ is Fréchet (2013, Glasner, Megrelishvili), or $G$ has countable $π$ -character (2022, Reznichenko) then $G$ is metrizable. Under the continuum hypothesis (CH) assumption, a sequentially compact CHART group is metrizable. Namioka's theorem that metrizable CHART groups are topological groups extends to CHART groups with small weight.