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On the length of chains of proper subgroups covering a topological group |
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| Authors: | Taras Banakh Du?an Repov? Lyubomyr Zdomskyy |
| Affiliation: | 1. Department of Mathematics, Ivan Franko National University of Lviv, Lviv, Ukraine 2. Instytut Matematyki, Uniwersytet Humanistyczno-Przyrodniczy, Jana Kochanowskiego w Kielcach, Kielce, Poland 3. Faculty of Mathematics and Physics, University of Ljubljana, P. O. Box 2964, 1001, Ljubljana, Slovenia 4. Faculty of Education, University of Ljubljana, P. O. Box 2964, 1001, Ljubljana, Slovenia 5. Kurt G?del Research Center for Mathematical Logic, University of Vienna, W?hringer Strasse 25, 1090, Wien, Austria |
| Abstract: | We prove that if an ultrafilter ${mathcal{L}}$ is not coherent to a Q-point, then each analytic non-??-bounded topological group G admits an increasing chain ${langle G_alpha:alpha < mathfrak b(mathcal L)rangle}$ of its proper subgroups such that: (i) ${bigcup_{alpha}G_alpha=G}$ ; and (ii) For every ??-bounded subgroup H of G there exists ?? such that ${Hsubset G_alpha}$ . In case of the group Sym(??) of all permutations of ?? with the topology inherited from ?? ?? this improves upon earlier results of S. Thomas. |
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