On the weight of nowhere dense subsets in compact spaces

We study a new cardinal-valued invariant $ndw(X)$ (calling it the $nd$-weight of $X$) of a topological space which is defined as the least upper bound of the weights of nowhere dense subsets of $X$. The main result is the proof of the inequality $hl(X)\leqslant ndw(X)$ for compact sets without isolated points (($hl$ is the hereditary Lindelöf number). This inequality implies that a compact space without isolated points of countable $nd$-weight is completely normal. Assuming the continuum hypothesis, we construct an example of a nonmetrizable compact space of countable $nd$-weight without isolated points.