joint work with T. Weiss

Speaker(s)

Michał Korch

Affiliation

doktorant UW

Date

Nov. 19, 2014, 4:15 p.m.

Room

room 5050

Title in Polish

The class of perfectly null sets and its transitive version

Seminar

Topology and Set Theory Seminar

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The ideals of universally null sets (UN, sets which are null with respect to any Borel diffused measure) and perfectly meager sets (PM, sets which are meager when restricted to any perfect set) are best known among the classes of special subsets of the real line. Those two ideals were long considered to be somehow dual, though some differences were also known. In 2000 Zakrzewski proved that two other earlier defined classes of sets smaller then PM coincide and are dual to UN. Therefore he proposed to call this class universally meager sets. The PM class was left without a counterpart, and we try to define a class of sets which may play the role of a dual class to PM and we also consider its transitive version. I will present some properties of those classes and give few important problems which are still open.

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