Normal nonmetrizable Moore space from continuum hypothesis or nonexistence of inner models with measurable cardinals

Abstract

Assuming the continuum hypothesis, a normal nonmetrizable Moore space is constructed. This answers a question raised by F. B. Jones in 1931, using an axiom well known at that time. For the construction, a consequence of the continuum hypothesis that also follows from the nonexistence of an inner model with a measurable cardinal is used. Hence, it is shown that to prove the consistency of the statement that all normal Moore spaces are metrizable one must assume the consistency of the statement that measurable cardinals exist.