Geodesic
Nowhere dense subsets and Booth's Lemma
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 2, pp. 391-395.

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The following statement is proved to be independent from $[\operatorname{LB}+\neg \operatorname{CH}]$: \linebreak $(*)$ Let $X$ be a Tychonoff space with $c(X)\leq \aleph _0$ and $\pi w(X)\frak C$. Then a union of less than $\frak C$ of nowhere dense subsets of $X$ is a union of not greater than $\pi w(X)$ of nowhere dense subsets.
Classification : 03E35, 03E50, 54A25, 54A35
Keywords: nowhere dense subset; Booth's Lemma; $\pi $-weight 
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Malykhin, V. I. Nowhere dense subsets and Booth's Lemma. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 2, pp. 391-395. http://geodesic.mathdoc.fr/item/CMUC_1996__37_2_a15/