On the class of NY compact spaces of finitely supported elements and related classes

2024/07/12 by Antonio Avilés, Avilés, Antonio, Mikołaj Krupski +1
Mathematics · #Advanced Banach Space Theory #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2407.09090

Abstract

We prove that a compact space K embeds into a σ-product of compact metrizable spaces (σ-product of intervals) if and only if K is (strongly countable-dimensional) hereditarily metalindelöf and every subspace of K has a nonempty relative open second-countable subset. This provides novel characterizations of ω-Corson and NY compact spaces. We give an example of a uniform Eberlein compact space that does not embed into a product of compact metric spaces in such a way that the σ-product is dense in the image. In particular, this answers a question of Kubiś and Leiderman. We also show that for a compact space K the property of being NY compact is determined by the topological structure of the space C_p(K) of continuous real-valued functions of K equipped with the pointwise convergence topology. This refines a recent result of Zakrzewski.

Related

• Function spaces on Corson-like compacta
• Digging into the classes of κ-Corson compact spaces
• A non-CLP-compact product space whose finite subproducts are CLP-compact
• Between countably compact and ω-bounded
• Every Lindelöf scattered subspace of a Σ-product of real lines is σ-compact