Abstract:We prove a dichotomy theorem for remainders in compactifications of homogeneous spaces: given a homogeneous space $X$, every remainder of $X$ is either realcompact and meager or Baire. In addition we show that two other recent dichotomy theorems for remainders of topological groups due to Arhangel'skii cannot be extended to homogeneous spaces.
Keywords: remainders in compactifications, homogeneous spaces
AMS Subject Classification: 54A25 54D35 54D40 54E52