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Sibirskii Matematicheskii Zhurnal, 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
References:
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
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 6, Pages 991–996
DOI: https://doi.org/10.1023/B:SIMJ.0000007474.56273.42
Bibliographic databases:
UDC: 515.12
Language: Russian
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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\paper On the weight of nowhere dense subsets in compact spaces
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\vol 44
\issue 6
\pages 1266--1272
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\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 6
\pages 991--996
\crossref{https://doi.org/10.1023/B:SIMJ.0000007474.56273.42}
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    Сибирский математический журнал Siberian Mathematical Journal
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