Cofinal types and topological groups. (English) Zbl 07919668
Summary: The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
MSC:
| 22A05 | Structure of general topological groups |
| 54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
| 03E04 | Ordered sets and their cofinalities; pcf theory |
References:
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| [2] | Dow, Alan; Feng, Ziqin, Compact spaces with a P-base, Indag. Math. (N. S.), 32, 4, 777-791, 2021 · Zbl 1480.54016 |
| [3] | Feng, Ziqin, P-bases and topological groups, Proc. Am. Math. Soc., 150, 2, 877-889, 2022 · Zbl 1494.22001 |
| [4] | Feng, Ziqin; Gartside, Paul, Directed sets of topology: Tukey representation and rejection, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., 118, 2, Article 44 pp., 2024 · Zbl 07836673 |
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| [8] | Solecki, Slawomir; Todorcevic, Stevo, Cofinal types of topological directed orders, Ann. Inst. Fourier (Grenoble), 54, 6, 1877-1911, 2004 · Zbl 1071.03034 |
| [9] | Todorcevic, Stevo, Basic orders in descriptive combinatorics, Topol. Appl., 323, Article 108300 pp., 2023 · Zbl 07628742 |
| [10] | Todorcevic, Stevo, Combinatorial dichotomies in set theory, Bull. Symb. Log., 17, 1, 1-72, 2011 · Zbl 1230.03075 |
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| [12] | Todorcevic, Stevo, P-ideal dichotomy and Tukey order, Fundam. Math., 2024, in press |
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