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 Sibirsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1266–1272 (Mi smj1253)

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

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English version:
Siberian Mathematical Journal, 2003, 44:6, 991–996

Bibliographic databases:

UDC: 515.12

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

Citation in format AMSBIB
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