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

• Autorzy: Mehrdad Karavan
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E55: Large cardinals
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54B05: Subspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 144
• Numer: 1
• Strony: 73-76

Daty

wydano

2016

Twórcy

autor

Mehrdad Karavan

• Department of Mathematics, Persian Gulf University, Mahini St., Bushehr, Iran
• Bushehr House of Mathematics, Farhang St., Bushehr, Iran

Identyfikatory

DOI

10.4064/cm6301-9-2015