Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces
Colloquium Mathematicum, Tome 144 (2016) no. 1, pp. 73-76
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Is it true in ZFC that every normal submaximal space of non-measurable cardinality is hereditarily realcompact? This question (posed by O. T. Alas et al. (2002)) is given a complete affirmative answer, for a wider class of spaces. In fact, this answer is a part of a bi-conditional statement: A normal nodec space $X$ is hereditarily realcompact if and only if it is realcompact if and only if every closed discrete (or nowhere dense) subset of $X$ has non-measurable cardinality.
Keywords:
zfc every normal submaximal space non measurable cardinality hereditarily realcompact question posed nbsp nbsp alas given complete affirmative answer wider class spaces answer part bi conditional statement normal nodec space hereditarily realcompact only realcompact only every closed discrete nowhere dense subset has non measurable cardinality
Affiliations des auteurs :
Mehrdad Karavan 1
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author = {Mehrdad Karavan},
title = {Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces},
journal = {Colloquium Mathematicum},
pages = {73--76},
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volume = {144},
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doi = {10.4064/cm6301-9-2015},
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%0 Journal Article %A Mehrdad Karavan %T Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces %J Colloquium Mathematicum %D 2016 %P 73-76 %V 144 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm6301-9-2015/ %R 10.4064/cm6301-9-2015 %G en %F 10_4064_cm6301_9_2015
Mehrdad Karavan. Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces. Colloquium Mathematicum, Tome 144 (2016) no. 1, pp. 73-76. doi: 10.4064/cm6301-9-2015
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