On the algebraic sum of a perfect set and a large subset of the reals

Speaker(s)

Tomasz Weiss

Affiliation

Cardinal Wyszyński University in Warsaw

Date

Oct. 13, 2021, 4:15 p.m.

Room

room 4420

Seminar

Topology and Set Theory Seminar

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In M. Kysiak’s paper "Nonmeasurable algebraic sums of sets of reals", (Coll. Math., Vol. 102, No 1, 2005), the following two questions appeared. Assume that A ⊆ R is a non-meager set with the Baire property and P is perfect. Do there exist meager sets X ⊆ A and Y ⊆ P such that X + Y is not meager? Suppose that A ⊆ R is a measurable set with positive measure and P is perfect. Do there exist measure zero sets X ⊆ A and Y ⊆ P such that X + Y is not null? Identifying R with the Cantor space 2^ω we answer both questions in the positive. ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

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Please note that the seminar will take place in lecture hall 4420. Also note that in the building of The Faculty of Mathematics, Informatics and Mechanics wearing face masks is mandatory.

 

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