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On the weight of nowhere dense subsets in compact spaces. (Russian, English) Zbl 1050.54003
Sib. Mat. Zh. 44, No. 6, 1266-1272 (2003); translation in Sib. Math. J. 44, No. 6, 991-996 (2003).
The author studies 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 $$hl(X)\leq ndw(X)$$ 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, the author constructs an example of a nonmetrizable compact space of countable $$nd$$-weight without isolated points.
##### MSC:
 54A05 Topological spaces and generalizations (closure spaces, etc.) 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54E35 Metric spaces, metrizability
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