Geodesic
Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces
Mehrdad Karavan1
1 Department of Mathematics Persian Gulf University Mahini St. Bushehr, Iran and Bushehr House of Mathematics Farhang St. Bushehr, Iran
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.
DOI : 10.4064/cm6301-9-2015
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

Mehrdad Karavan 1

1 Department of Mathematics Persian Gulf University Mahini St. Bushehr, Iran and Bushehr House of Mathematics Farhang St. Bushehr, Iran 
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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. http://geodesic.mathdoc.fr/articles/10.4064/cm6301-9-2015/

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