March 2015
Oleg Gutik: Around the bicyclic monoid: topological and semigroup views
26/03/15 17:33
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.
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
23/03/15 20:46
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.
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
11/03/15 17:35
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.
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
09/03/15 10:48
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.
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.