BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

Tukey reducibility and metrizable groups Guevara Parra, Francisco


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}

Item Media

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International