Discrete Sets of Singular Cardinality

Abstract

Let « be a singular cardinal. In Fleissner's thesis, he showed that in normal spaces X, certain discrete sets Y of cardinality a (called here sparse) which are < ic-separated are, in fact, separated. In Watson's thesis, he proves the same for countably paracompact spaces X. Here we improve these results by making no assumption on the space X. As a corollary, we get that assuming V = L, S,-paralindelöf 7", spaces of character « co, are collectionwise Hausdorff.