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Tukey reducibility and metrizable groups

Banff International Research Station for Mathematical Innovation and Discovery

In [4] the authors used the Local Ramsey theory to prove that a countable Frechet group is metrizable if, and only if, its topology is analytic. We use this result together with the connections between the Tukey ordering and topology found in [2] to give a characterization of separable metrizable groups. We prove that a separable group is metrizable if, and only if, it is Frechet and the the ideal of converging sequences to the identity is Tukey below some basic order that is analytic. Results in this direction have been obtained before in [1].
[1] S. Gabriyelyan, J. Kakol and A. Leiderman. On topological groups with a small base and metrizability. Fundamenta Mathematicae, 229 (2015) 129-157.
[2] S. Solecki and S. Todorcevic. Cofinal types of topological directed orders. Ann. Inst. Fourier, Grenoble, 54, 6 (2004), 1877-1911.
[3] S. Todorcevic. Introduction to Ramsey spaces. Annals of Mathematics Studies, No 174, Princeton, 2010.
[4] S. Todorcevic and C. Uzcategui. Analytic $k$-spaces. Topology and its applications, 146-147 (2005) 511-526. \end{thebibliography}

Mathematics; Mathematical logic and foundations; Combinatorics

video/mp4

Author affiliation: University of Toronto

2019-05-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/70239

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/