Digging into the classes of κ-Corson compact spaces

2021/07/06 by Marciszewski, Witold, Plebanek, Grzegorz, Zakrzewski, Krzysztof
#46A50 #54D30 #54G12 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2107.02513

Abstract

For any cardinal number κ and an index set Γ, Σ_κ-product of real lines consists of elements of \mathbb R^Γ having <κ nonzero coordinates. A compact space K is κ-Corson compact if it can be embedded into such a space for some Γ. The class of (ω₁-)Corson compact spaces has been intensively studied over last decades. We discuss properties of κ-Corson compacta for various cardinal numbers κ as well as properties of related Boolean algebras and spaces of continuous functions. We present here a detailed discussion of the class of ω-Corson compacta extending the results of Nakhmanson and Yakovlev. For κ>ω, our results on κ-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 recent paper.

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