Digging into the classes of $\kappa$-Corson compact spaces
Witold Marciszewski, Grzegorz Plebanek, Krzysztof Zakrzewski

TL;DR
This paper explores the properties of $$-Corson compact spaces for various cardinals, extending previous research and analyzing related Boolean algebras and function spaces.
Contribution
It provides a detailed analysis of $$-Corson compacta, extending known results for $$-Corson spaces and connecting them with recent developments in the field.
Findings
Extended results on $$-Corson compacta for various $$
Analyzed properties of related Boolean algebras and continuous function spaces
Connected findings with recent research by Kalenda, Bell, Marciszewski, Bonnet, Kubis, and Todorcevic.
Abstract
For any cardinal number and an index set , -product of real lines consists of elements of having nonzero coordinates. A compact space is -Corson compact if it can be embedded into such a space for some . The class of (-)Corson compact spaces has been intensively studied over last decades. We discuss properties of -Corson compacta for various cardinal numbers as well as properties of related Boolean algebras and spaces of continuous functions. We present here a detailed discussion of the class of -Corson compacta extending the results of Nakhmanson and Yakovlev. For , our results on -Corson compact spaces are related to the line of research originated by Kalenda and Bell and Marciszewski, and continued by Bonnet, Kubis and Todorcevic in their…
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Homotopy and Cohomology in Algebraic Topology
