Adam Kwela: Unboring ideals
06/05/21 18:05
Tuesday, May 11, 2021 17:00
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Adam Kwela (University of Gdańsk)
Title: Unboring ideals
Abstract: We say that a space \(X\) is \(FinBW(I)\) (\(I\) is an ideal on the set of natural numbers), if for each sequence \((x_n)\) in \(X\) one can find a set \(A\) not belonging to \(I\) such that \((x_n)_{n\in A}\) converges in \(X\). Thus, the classical Bolzano-Weierstrass theorem states that every compact subset of the real line is \(FinBW(Fin)\) (\(Fin\) is the ideal of all finite subsets of naturals). During my talk I will present new results concerning \(FinBW(I)\) spaces and discuss relationship between the studied notions and the Katetov order on ideals. In particular, under \(MA\) I will characterize for all \(\Pi^0_4\) ideals when \(FinBW(I)\) and \(FinBW(J)\) differ.
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Adam Kwela (University of Gdańsk)
Title: Unboring ideals
Abstract: We say that a space \(X\) is \(FinBW(I)\) (\(I\) is an ideal on the set of natural numbers), if for each sequence \((x_n)\) in \(X\) one can find a set \(A\) not belonging to \(I\) such that \((x_n)_{n\in A}\) converges in \(X\). Thus, the classical Bolzano-Weierstrass theorem states that every compact subset of the real line is \(FinBW(Fin)\) (\(Fin\) is the ideal of all finite subsets of naturals). During my talk I will present new results concerning \(FinBW(I)\) spaces and discuss relationship between the studied notions and the Katetov order on ideals. In particular, under \(MA\) I will characterize for all \(\Pi^0_4\) ideals when \(FinBW(I)\) and \(FinBW(J)\) differ.