On the Weight of Nowhere Dense Subsets in Compact Spaces.

We study a new cardinal-valued invariant <MATH>ndw(X)</MATH> (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)≤ndw(X) for compact sets without isolated points ((hl is the hereditary Lindelof 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. [ABSTRACT FROM AUTHOR]