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Nowhere dense subsets and Booth’s lemma. (English) Zbl 0854.54005
Summary: The following statement is proved to be independent from \([\text{LB} +\neg \text{CH}]\): Let \(X\) be a Tikhonov space with \(c(X)\leq \aleph_0\) and \(\pi w(X)< {\mathfrak C}\). Then a union of less than \({\mathfrak C}\) of nowhere dense subsets of \(X\) is a union of not more than \(\pi w(X)\) of nowhere dense subsets.

MSC:
54A35 Consistency and independence results in general topology
03E35 Consistency and independence results
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
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