About remainders in compactifications of paratopological groups

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.