An internal topological characterization of the subspaces of Eberlein compacts and related compacts -- I

TL;DR

This paper provides an internal topological characterization of various subspaces of Eberlein compact spaces, including Corson, strong Eberlein, uniform Eberlein, and n-uniform Eberlein compacts, enhancing understanding of their structure.

Contribution

It introduces a novel internal topological framework that characterizes subspaces of Eberlein and related compact spaces, advancing the theoretical understanding of these classes.

Findings

Characterization of subspaces of Eberlein compacts

Extension to Corson and strong Eberlein compacts

Framework applicable to uniform and n-uniform Eberlein compacts

Abstract

We obtain an internal topological characterization of the subspaces of Eberlein compacts (respectively, Corson compacts, strong Eberlein compacts, uniform Eberlein compacts, $n$-uniform Eberlein compacts).