April 2024

# Tomasz Żuchowski: The Nikodym property and filters on \(\omega\). Part II

22/04/24 08:20

Tuesday, April 23, 2024 17:15

In this talk we will study the family \(\mathcal{AN}\) of such ideals \(\mathcal{I}\) on \(\omega\) that the space \(N_{\mathcal{I}^*}\) carries a sequence \(\langle\mu_n\colon n\in\omega\rangle\) of finitely supported signed measures satisfying \(\|\mu_n\|\rightarrow\infty\) and \(\mu_n(A)\rightarrow 0\) for every \(A\in Clopen(N_{\mathcal{I}^*})\). If \(\mathcal{I}\in\mathcal{AN}\) and \(N_{\mathcal{I}^*}\) is embeddable into the Stone space \(St(\mathcal{A})\) of a given Boolean algebra \(\mathcal{A}\), then \(\mathcal{A}\) does not have the Nikodym property.

*Location:*A.4.1 C-19*Tomasz Żuchowski*

Speaker:Speaker:

*Title*: The Nikodym property and filters on \(\omega\). Part II*Abstract*: For a free filter \(F\) on \(\omega\), we consider the space \(N_F=\omega\cup\{p_F\}\), where every element of \(\omega\) is isolated and open neighborhoods of \(p_F\) are of the form \(A\cup\{p_F\}\) for \(A\in F\).In this talk we will study the family \(\mathcal{AN}\) of such ideals \(\mathcal{I}\) on \(\omega\) that the space \(N_{\mathcal{I}^*}\) carries a sequence \(\langle\mu_n\colon n\in\omega\rangle\) of finitely supported signed measures satisfying \(\|\mu_n\|\rightarrow\infty\) and \(\mu_n(A)\rightarrow 0\) for every \(A\in Clopen(N_{\mathcal{I}^*})\). If \(\mathcal{I}\in\mathcal{AN}\) and \(N_{\mathcal{I}^*}\) is embeddable into the Stone space \(St(\mathcal{A})\) of a given Boolean algebra \(\mathcal{A}\), then \(\mathcal{A}\) does not have the Nikodym property.

# Krzysztof Zakrzewski: Function spaces on Corson-like compacta

13/04/24 07:08

Tuesday, April 16, 2024 17:15

Every \(\omega\)-Corson compact space is Eberlein compact. For a Tichonoff space \(X\), let \(C_p(X)\) denote the space of real continuous functions on \(X\) endowed with the pointwise convergence topology.

During the talk we will show that the class \(\omega\)-Corson compact spaces \(K\) is invariant under linear homeomorphism of function spaces \(C_p(K)\) and other related results.

*Location:*A.4.1 C-19*Krzysztof Zakrzewski (MIM UW)*

Speaker:Speaker:

*Title*: Function spaces on Corson-like compacta*Abstract*: Recall that a compact space is Eberlein compact if it is homeomorphic to a subspace of some Banach space equipped with the weak topology. A compact space is \(\omega\)-Corson compact if it embeds into a \(\sigma\)-product of real lines, that is a subspace of the product \(R^{\Gamma}\) consisting of sequences with finitely many nonzero coordinates for some set \(\Gamma\).Every \(\omega\)-Corson compact space is Eberlein compact. For a Tichonoff space \(X\), let \(C_p(X)\) denote the space of real continuous functions on \(X\) endowed with the pointwise convergence topology.

During the talk we will show that the class \(\omega\)-Corson compact spaces \(K\) is invariant under linear homeomorphism of function spaces \(C_p(K)\) and other related results.

# Jakub Rondos

04/04/24 11:16

Tuesday, April 9, 2024 17:15

will be presented by

*Location:*A.4.1 C-19*Jakub Rondos (University of Vienna)*

Speaker:Speaker:

*Title*: Topological properties of compact spaces K that are preserved by isomorphisms of C(K)"will be presented by

*Abstract*: In the talk, we present some newly discovered properties of compact Hausdorff spaces that are preserved by isomorphisms of their Banach spaces of continuous functions.