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

Mehrdad Karavan. "Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces." Colloquium Mathematicae 144.1 (2016): 73-76. <http://eudml.org/doc/286075>.

@article{MehrdadKaravan2016,
abstract = {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.},
author = {Mehrdad Karavan},
journal = {Colloquium Mathematicae},
keywords = {submaximal; nodec; realcompact},
language = {eng},
number = {1},
pages = {73-76},
title = {Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces},
url = {http://eudml.org/doc/286075},
volume = {144},
year = {2016},
}

TY - JOUR
AU - Mehrdad Karavan
TI - Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces
JO - Colloquium Mathematicae
PY - 2016
VL - 144
IS - 1
SP - 73
EP - 76
AB - 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.
LA - eng
KW - submaximal; nodec; realcompact
UR - http://eudml.org/doc/286075
ER -