A provisional solution to the normal Moore space problem
Author:
Peter J. Nyikos
Journal:
Proc. Amer. Math. Soc. 78 (1980), 429435
MSC:
Primary 54E30; Secondary 03E35, 54A35
DOI:
https://doi.org/10.1090/S00029939198005533894
MathSciNet review:
553389
Fulltext PDF Free Access
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 wellknown 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
Keywords:
Moore space,
collectionwise normal,
normalized,
well separated,
Product Measure Extension Axiom,
metrizable,
strongly compact
Article copyright:
© Copyright 1980
American Mathematical Society