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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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