March 2015

Oleg Gutik: Around the bicyclic monoid: topological and semigroup views

Wednesday, April 1, 2015 17:15

Room: D1-215

Speaker:
Oleg Gutik

Title: Around the bicyclic monoid: topological and semigroup views

Abstract. We discuss algebraic and topological properties of (semitopological and topological) semigroups which are close to the bicyclic monoid: the semigroup of matrix units, the semigroup of co-finite partial bijections and the polycyclic monoid. We speak about topologizations of such semigroups as topological or semitopological semigroups, their embeddings into compact-like topological semigroups and their closures in topological semigroups.

Robert Rałowski: Two point sets, continuation

Tuesday, March 24, 2015 17:15

Room: D1-215

Speaker:
Robert Rałowski

Title: Two point sets, continuation

Abstract. We will continue discussion started a week ago concerning two point sets. We will give another example of a property of two point set which is consistent with ZFC.

Robert Rałowski: Cohen indestructible mad families in partial two point sets

Tuesday, March 17, 2015 17:15

Room: D1-215

Speaker:
Robert Rałowski

Title: Cohen indestructible mad families in partial two point sets

Abstract. We discuss on classical construction of Cohen indestructible mad family given by Kenneth Kunen and we apply this method to obtain a partial Cohen indestructible mad family in Baire space as a canonical copy of the real plane.

Marcin Michalski: Avoiding rational distances

Tuesday, March 10, 2015 17:15

Room: D1-215

Speaker:
Marcin Michalski

Title: Avoiding rational distances

Abstract. We shall present results obtained by Ashutosh Kumar in paper "Avoiding rational distances". The author showed that for any set of reals X of positive outer measure there exists a subset Y of X such that Y has the same outer measure and the distance between any distinct points of Y is irrational. We will also discuss briefly the case of higher dimensions.