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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)
##### Keywords:
nowhere dense subset; Booth’s lemma; $$\pi$$-weight
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