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Keywords:
extremally disconnected and maximal spaces; semitopological group; Stone-Čech compactification
extremally disconnected and maximal spaces; semitopological group; Stone-Čech compactification
Summary:
Answering recent question of A.V. Arhangel'skii we construct in ZFC an extremally disconnected semitopological group with continuous inverse having no open Abelian subgroups.
References:
[1] Arhangel'skii A.V.: On topological and algebraic properties of extremally disconnected semitopological groups. Comment. Math. Univ. Carolinae 42.4 (2000), 803-810. MR 1800164
[2] Arhangel'skii A.V.: Groups topologiques extremalement discontinus. C.R. Acad. Sci. Paris 265 (1967), 822-825. MR 0222207
[3] Hindman N., Strauss D.: Algebra in the Stone-Čech Compactification: Theory and Applications. Walter de Gruyter, Berlin, 1998. MR 1642231 | Zbl 0918.22001
[4] Protasov I.V.: Filters and topologies on semigroups (in Russian). Mat. Stud. 3 (1994), 15-28. MR 1692845
[5] Protasov I.V.: Maximal topologies on groups. Siberian Math. J. 39 (1998), 1184-1194. MR 1672661 | Zbl 0935.22002
[6] Protasov I.V.: On maximal topologies on groups. Visn. Kyiv. Univ. Ser. Fiz-mat. nauk, no. 3 (1998), 251-253. MR 1672661
[7] Protasov I.V.: Indecomposable topologies on groups. Ukrainian Math. J. 50 (1998), 1879-1887. MR 1721072
[8] Protasov I.V.: Extremal topologies on groups. Mat. Stud. 15 (2001), 9-22. MR 1871923 | Zbl 0989.22003
[9] Zelenyuk E.G.: Extremal ultrafilters and topologies on groups (in Russian). Mat. Stud. 14 (2000), 121-140. MR 1813995
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