Discrete sets of singular cardinality
Abstract: Let be a singular cardinal. In Fleissner's thesis, he showed that in normal spaces , certain discrete sets of cardinality (called here sparse) which are -separated are, in fact, separated. In Watson's thesis, he proves the same for countably paracompact spaces . Here we improve these results by making no assumption on the space . As a corollary, we get that assuming , ,-paralindelöf , spaces of character , are collectionwise Hausdorff.
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Keywords: Discrete, singular cardinals, collectionwise Hausdorff
Article copyright: © Copyright 1983 American Mathematical Society