Almost paratopological groups

2023/06/09 by Reznichenko, Evgenii
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2306.06241

Abstract

A class of almost paratopological groups is introduced, which (1) contains paratopological groups and Hausdorff quasitopological groups; (2) is closed under products; (3) subgroups. Almost paratopological T₁ groups G are characterized by the fact that \(x,y)∈ G²: xy=e\ is closed in G². A compact almost paratopological group is topological. A regular Σ-space with a countable extend and a separately continuous Mal'tsev operation is ω-cellular (and ccc). A σ-compact regular almost paratopological group is ccc. In particular, a σ-compact regular quasitopological group is ccc.

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