Abstract:The following statement is proved to be independent from $[LB+\neg CH]$: $(*)$ 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.
Keywords: nowhere dense subset, Booth's Lemma, $\pi $-weight
AMS Subject Classification: Primary 54A35, 03E35; Secondary 54A25