Compact condensations of Hausdorff spaces
Vitalii I. Belugin, Alexander V. Osipov, Evgenii G. Pytkeev

TL;DR
This paper investigates conditions under which Hausdorff spaces can be condensed onto compact spaces, focusing on the properties of subsets and their cardinalities, to extend classical topology results.
Contribution
It extends the understanding of condensations of Hausdorff spaces onto compacta, especially considering subsets with bounded cardinality.
Findings
Conditions for condensations onto compacta are characterized.
The role of subset cardinalities in condensation properties is clarified.
New classes of Hausdorff spaces with condensation properties are identified.
Abstract
In this paper, we continue to study one of the classic problems in general topology raised by P.S. Alexandrov: when a Hausdorff space has a continuous bijection (a condensation) onto a compactum? We concentrate on the situation when not only but also can be condensed onto a compactum whenever the cardinality of does not exceed certain .
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