On perfect monochromatic sets in analytic spaces

Speaker(s)

Wiesław Kubiś

Affiliation

Jan Kochanowski University in Kielce and Mathematical Institute of the Czech Academy of Sciences

Date

March 11, 2015, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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It is known that if C is a G-delta symmetric relation in an analytic space and there exists an uncountable C-monochromatic set then there exists also a perfect one. We extend this result to the case of countably many G-delta relations, in the same spirit as Mycielski's theorem.
As an application, we obtain the following: If G is a Polish group containing a nonempty dense-in-itslef set generating a free subgroup, then G contains a free subgroup generated by a perfect set.

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