Submaximal properties in (strongly) topological gyrogroups

TL;DR

This paper investigates properties of submaximal topological gyrogroups, proving they are strongly σ-discrete and hereditarily paracompact under certain conditions related to their cardinality.

Contribution

It establishes new topological properties of submaximal (strongly) topological gyrogroups, linking submaximality with strong σ-discreteness and hereditary paracompactness.

Findings

Submaximal topological gyrogroups of non-measurable cardinality are strongly σ-discrete.

Submaximal strongly topological gyrogroups of non-measurable cardinality are hereditarily paracompact.

Abstract

A space $X$ is submaximal if any dense subset of $X$ is open. In this paper, we prove that every submaximal topological gyrogroup of non-measurable cardinality is strongly $\sigma$-discrete. Moreover, we prove that every submaximal strongly topological gyrogroup of non-measurable cardinality is hereditarily paracompact.