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.
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机译：假设连续假设，则构造了一个正常的不可度量的摩尔空间。这使用了当时众所周知的公理回答了F. B. Jones在1931年提出的一个问题。对于构造，使用了连续性假设的结果，该假设也源于不存在可测量基数的内部模型。因此，表明要证明所有正常Moore空间都是可度量的陈述的一致性，必须假设存在可测基数的陈述的一致性。
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