Abstract
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)≤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.
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Ivanov, A.V. On the Weight of Nowhere Dense Subsets in Compact Spaces. Siberian Mathematical Journal 44, 991–996 (2003). https://doi.org/10.1023/B:SIMJ.0000007474.56273.42
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DOI: https://doi.org/10.1023/B:SIMJ.0000007474.56273.42