About remainders in compactifications of paratopological groups

TL;DR

This paper establishes a dichotomy for remainders in compactifications of paratopological groups, showing they are either Lindelöf and meager or Baire, and addresses related open questions.

Contribution

It proves a new dichotomy theorem for remainders in compactifications of paratopological groups and provides a negative answer to a previously posed question.

Findings

Remainders are either Lindelöf and meager or Baire

Negative answer to Basile and Bella's question

Poses new open questions about remainders

Abstract

In this paper, we prove a dichotomy theorem for remainders in compactifications of paratopological groups: every remainder of a paratopological group $G$ is either Lindel\"{o}f and meager or Baire. Moreover, we give a negative answer for a question posed by D. Basile and A. Bella in \cite{B1}, and some questions about remainders of paratopological groups are posed in the paper.