Characterizing meager paratopological groups

TL;DR

This paper characterizes meager Hausdorff paratopological groups by showing they can be generated by a nowhere dense set and a countable set through group operations.

Contribution

It provides a necessary and sufficient condition for meagerness in Hausdorff paratopological groups involving nowhere dense and countable subsets.

Findings

A Hausdorff paratopological group is meager iff it can be expressed as CA=G=AC with A nowhere dense and C countable.

The characterization links topological size (meagerness) to algebraic structure.

The result offers a new perspective on the structure of meager paratopological groups.

Abstract

We prove that a Hausdorff paratopological group G is meager if and only if there are a nowhere dense subset A of G and a countable subset C in G such that CA=G=AC.