Arhangel’skii, A. V. Two types of remainders of topological groups. (English) Zbl 1212.54086 Commentat. Math. Univ. Carol. 49, No. 1, 119-126 (2008). Summary: 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 Dieudonné complete, then the remainder is Lindelöf, and the group is a paracompact \(p\)-space. This answers a question in A. V. Arkhangel’skij [Mosc. Univ. Math. Bull. 54, No. 3, 1–6 (1999); translation from Vestn. Mosk. Univ., Ser. I 1999, No. 3, 4–10 (1999; Zbl 0949.54054)]. 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. Cited in 6 ReviewsCited in 29 Documents MSC: 54D40 Remainders in general topology 54H11 Topological groups (topological aspects) 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54C25 Embedding Keywords:remainder; compactification; topological group; \(p\)-space Citations:Zbl 0949.54054 PDFBibTeX XMLCite \textit{A. V. Arhangel'skii}, Commentat. Math. Univ. Carol. 49, No. 1, 119--126 (2008; Zbl 1212.54086) Full Text: EuDML EMIS