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About remainders in compactifications of paratopological groups

Article 12, Volume 40, Issue 3, June 2014, Page 713-719  XML PDF (99 K)
Document Type: Research Paper
Authors
Fucai Lin 1; Shou Lin2
1Minnan Normal University
2Ningde Teachers' College
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. 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.
Keywords
Remainders‎; ‎paratopological groups‎; ‎topological groups‎; ‎homogeneous spaces‎; ‎Baire spaces‎
Main Subjects
22-XX Topological groups, Lie groups; 54-XX General topology
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