TL;DR
This paper investigates the minimum number of discrete sets needed to cover compact spaces, exploring relationships with free sequences and space cardinality, and providing partial positive answers to a specific open question.
Contribution
It offers new bounds and insights into the interplay between discrete sets, free sequences, and the size of Hausdorff spaces, advancing understanding in this area.
Findings
Improved bounds on the number of discrete sets covering compact spaces
Established relationships between free sequences and space cardinality
Provided partial positive answers to Juhasz and Szentmiklossy's question
Abstract
We give several partial positive answers to a question of Juhasz and Szentmiklossy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Algebra and Logic · semigroups and automata theory