Year: 2025
Type: article
Abstract: We prove that a compact space embeds into a ‐product of compact metrizable spaces (‐product of intervals) if and only if is (strongly countable‐dimensional) hereditarily metalindelöf and every subspace of has a nonempty relative open second countable subset. This provides novel characterizations of ‐Corson and 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 ‐product is dense in the image. In particular, this answers a question of Kubiś and Leiderman. We also show that for a compact space , the property of being compact is determined by the topological structure of the space of continuous real‐valued functions of equipped with the pointwise convergence topology. This refines a recent result of Zakrzewski.
DOI: 10.1112/blms.70058
Authors: Antonio Avilés, Mikołaj Krupski
Institutions: Universidad de Murcia, University of Warsaw
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4409170834