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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Sem. Topologia i T. Mnogości

 

Automatic continuity of measurable homomorphisms on topological groups


Prelegent: Taras Banakh

2022-01-26 16:15

We shall discuss three recent results on automatic continuity of homomorphisms:
1) Every Haar-measurable homomorphism from a locally compact group to an arbitrary topological group is continuous.
2) Every homomorphism with the Baire property from an $\omega$-narrow Cech-complete topological group to an arbitrary topological group is continuous
3) Every Borel homomorphism from a Cech-complete topological group to an arbitrary topological group is continuous. 
The continuity of Haar-measurable homomorphisms on locally compact groups was proved by Kuznetsova in 2012 under Martin's Axiom. Our proofs are based on a new result about analytically nonmeasurable unions of sets in $\sigma$-ideals on Polish spaces, 
which was obtained jointly with Ralowski and Zeberski.