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On α -normal and β -normal spaces

Aleksander V. Arhangel'skiiLewis D. Ludwig — 2001

Commentationes Mathematicae Universitatis Carolinae

We define two natural normality type properties, α -normality and β -normality, and compare these notions to normality. A natural weakening of Jones Lemma immediately leads to generalizations of some important results on normal spaces. We observe that every β -normal, pseudocompact space is countably compact, and show that if X is a dense subspace of a product of metrizable spaces, then X is normal if and only if X is β -normal. All hereditarily separable spaces are α -normal. A space is normal if and...

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