A provisional solution to the normal Moore space problem

Author:
Peter J. Nyikos

Journal:
Proc. Amer. Math. Soc. **78** (1980), 429-435

MSC:
Primary 54E30; Secondary 03E35, 54A35

DOI:
https://doi.org/10.1090/S0002-9939-1980-0553389-4

MathSciNet review:
553389

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Abstract | References | Similar Articles | Additional Information

Abstract: The Product Measure Extension Axiom (PMEA), whose consistency would follow from the existence of a strongly compact cardinal, implies that every normalized collection of sets in a space of character less than the continuum is well separated. Consistency of PMEA would thus solve many well-known problems of general topology, including that of whether every first countable normal space is collectionwise normal, as well as the normal Moore space problem.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0553389-4

Keywords:
Moore space,
collectionwise normal,
normalized,
well separated,
Product Measure Extension Axiom,
metrizable,
strongly compact

Article copyright:
© Copyright 1980
American Mathematical Society