On some kinds of factorizable topological groups

TL;DR

This paper introduces four new classes of factorizability in topological groups based on existing concepts, and explores their properties to deepen understanding of their structure.

Contribution

It defines four new classes of factorizability in topological groups and investigates their properties, expanding the theoretical framework.

Findings

Four classes of factorizability are introduced.

Properties of these classes are systematically studied.

The work advances the theoretical understanding of factorizable topological groups.

Abstract

Based on the concepts of $\mathbb{R}$-factorizable topological groups and $\mathcal{M}$-factorizable topological groups, we introduce four classes of factorizabilities on topological groups, named $P\mathcal{M}$-factorizabilities, $Pm$-factorizabilities, $S\mathcal{M}$-factorizabilities and $PS\mathcal{M}$-factorizabilities, respectively. Some properties of the four classes of spaces are investigated.