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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 6, Pages 1266–1272
(Mi smj1253)
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On the weight of nowhere dense subsets in compact spaces
A. V. Ivanov Petrozavodsk State University
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 $hl(X)\leqslant ndw(X)$ 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.
Keywords:
compact space, nowhere dense set, hereditary Lindelöf number, $nd$-weight.
Received: 31.03.2003
Citation:
A. V. Ivanov, “On the weight of nowhere dense subsets in compact spaces”, Sibirsk. Mat. Zh., 44:6 (2003), 1266–1272; Siberian Math. J., 44:6 (2003), 991–996
Linking options:
https://www.mathnet.ru/eng/smj1253 https://www.mathnet.ru/eng/smj/v44/i6/p1266
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Abstract page: | 322 | Full-text PDF : | 84 | References: | 61 |
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