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
(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.