Witold Marciszewski: On \(\omega\)-Corson compact spaces and related classes of Eberlein compacta
02/11/23 10:39
Friday, November 3, 2023 16:15
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Witold Marciszewski (MIM UW)
Title: On \(\omega\)-Corson compact spaces and related classes of Eberlein compacta
Abstract: Recall that a compact space \(K\) is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology; equivalently, for some set \(\Gamma\), \(K\) can be embedded into the space \(c_0( \Gamma)\), endowed with the pointwise convergence topology.
A compact space \(K\) is \(\omega\)-Corson compact if, for some set \(\Gamma\), \(K\) is homeomorphic to a subset of the \(\sigma\)-product of real lines \(\sigma(\mathbb{R}^\Gamma)\), i.e. the subspace of the product \(\mathbb{R}^\Gamma\) consisting of functions with finite supports. Clearly, every \(\omega\)-Corson compact space is Eberlein compact.
We will present a characterization of \(\omega\)-Corson compact spaces, and some other results concerning this class of spaces and related classes of Eberlein compacta.
This is a joint research with Grzegorz Plebanek and Krzysztof Zakrzewski, see
https://arxiv.org/abs/2107.02513
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Witold Marciszewski (MIM UW)
Title: On \(\omega\)-Corson compact spaces and related classes of Eberlein compacta
Abstract: Recall that a compact space \(K\) is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology; equivalently, for some set \(\Gamma\), \(K\) can be embedded into the space \(c_0( \Gamma)\), endowed with the pointwise convergence topology.
A compact space \(K\) is \(\omega\)-Corson compact if, for some set \(\Gamma\), \(K\) is homeomorphic to a subset of the \(\sigma\)-product of real lines \(\sigma(\mathbb{R}^\Gamma)\), i.e. the subspace of the product \(\mathbb{R}^\Gamma\) consisting of functions with finite supports. Clearly, every \(\omega\)-Corson compact space is Eberlein compact.
We will present a characterization of \(\omega\)-Corson compact spaces, and some other results concerning this class of spaces and related classes of Eberlein compacta.
This is a joint research with Grzegorz Plebanek and Krzysztof Zakrzewski, see
https://arxiv.org/abs/2107.02513