2011 seminar talk: The character of topological groups, via Pontryagin-van Kampen duality and pcf theory

Talk held by Boaz Tsaban (Bar-Ilan University, Israel) at the KGRC seminar on 2011-09-14.


The Birkhoff-Kakutani Theorem asserts that a topological group is metrizable if and only if it has countable character. We develop and apply tools for the estimation of the character for a wide class of nonmetrizable topological groups. Even in the special case of free abelian topological groups, our results extend a number of results of Nickolas and Tkachenko, which were proved using laborious elementary methods.

Our method use a novel combination of (classical) descriptive set theory, Pontryagin-van Kampen duality, and pcf theory.

I will not assume knowledge of topological groups or any of the topics mentioned in the abstract or used in the talk. Students are, in particular, welcome.

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.