Abstract:We give several partial positive answers to a question of Juhász and Szentmikl\'ossy 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.
Keywords: discrete set, dispersion character, compact space, Eberlein compact, free sequence, elementary submodel
AMS Subject Classification: 54A25