Krzysztof Zakrzewski: Function spaces on Corson-like compacta
13/04/24 07:08
Tuesday, April 16, 2024 17:15
Location: A.4.1 C-19
Speaker: Krzysztof Zakrzewski (MIM UW)
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.
Location: A.4.1 C-19
Speaker: Krzysztof Zakrzewski (MIM UW)
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.