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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: 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

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