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Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces

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Karavan M.

Colloquium Mathematicum

2016

tom 144

nr 1

73-76

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.

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1 Colloquium Mathematicum

1 Karavan M.

1 2016

Wyniki wyszukiwania

Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces