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 Lindelof and meager or‎ ‎Baire‎. ‎Furthermore‎, ‎we give a negative answer to a question posed in‎ ‎[D‎. ‎Basile and A‎. ‎Bella‎, ‎About remainders in compactifications of homogeneous spaces‎, ‎{Comment‎. ‎Math‎. ‎Univ‎. ‎Carolin.} {50} (2009)‎, ‎no‎. ‎4‎, ‎607--613]‎. ‎Some questions about‎ ‎remainders in compactifications of paratopological groups are posed‎.