Dear all,

The seminar meets on Wednesday September 19th at 11:00 in the Institute

of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Michał Korch — The class of perfectly null sets and its

transitive version

(joint work with Tomasz Weiss)

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. P. 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 am going to present some properties

of these classes and give few important problems which are still open

along with some new attempts and simplifications to get an answer.

Best,

David