Stationary Sets in Topological and Paratopological Groups

TL;DR

This paper investigates the properties of topological and paratopological groups containing stationary sets, demonstrating that such groups have non-collectionwise normal subspaces and that certain normal spaces are hereditarily paracompact.

Contribution

It establishes a link between stationary sets in groups and their normality properties, showing that certain normal spaces within these groups are hereditarily paracompact.

Findings

Presence of stationary sets implies non-collectionwise normal subspaces.

Monotonically normal paratopological groups are hereditarily paracompact.

Generalized ordered spaces as paratopological groups are hereditarily paracompact.

Abstract

We show that if a topological or paratopological group $G$ contains a stationary subset of some regular uncountable cardinal, then $G$ contains a subspace which is not collectionwise normal. This statement implies that if a monotonically normal space (in particular, any generalized ordered space) is a paratopological group then the space is hereditarily paracompact.