Geodesic
Two types of remainders of topological groups
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 119-126

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We prove a Dichotomy Theorem: for each Hausdorff compactification $bG$ of an arbitrary topological group $G$, the remainder $bG\setminus G$ is either pseudocompact or Lindelöf. It follows that if a remainder of a topological group is paracompact or Dieudonne complete, then the remainder is Lindelöf, and the group is a paracompact $p$-space. This answers a question in A.V. Arhangel'skii, {\it Some connections between properties of topological groups and of their remainders\/}, Moscow Univ. Math. Bull. 54:3 (1999), 1--6. It is shown that every Tychonoff space can be embedded as a closed subspace in a pseudocompact remainder of some topological group. We also establish some other results and present some examples and questions.
Classification : 54A25, 54B05
Keywords: remainder; compactification; topological group; $p$-space; Lindelöf $p$-space; metrizability; countable type; Lindelöf space; pseudocompact space; $\pi $-base; compactification 
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Arhangel'skii, A. V. Two types of remainders of topological groups. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 119-126. http://geodesic.mathdoc.fr/item/CMUC_2008__49_1_a10/