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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.

A provisional solution to the normal Moore space problem