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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An extension of Morita's metrization theorem


Author: Charles C. Alexander
Journal: Proc. Amer. Math. Soc. 30 (1971), 578-582
MSC: Primary 54.35
DOI: https://doi.org/10.1090/S0002-9939-1971-0286069-8
MathSciNet review: 0286069
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Abstract: Morita proved that metrizability of a $ {T_0}$ space is equivalent to the existence of a sequence of locally finite closed covers which satisfies a refinement condition. We introduce the definition of a cushioned pair-semidevelopment and prove that the existence of a cushioned pair-semidevelopment in a $ {T_0}$ space is equivalent to the metrizability of the space. In addition to Morita's theorem, it is seen that several other well-known metrization theorems are also immediate corollaries to the new theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0286069-8
Keywords: Semidevelopable, cushioned pair-semidevelopment, metrizable
Article copyright: © Copyright 1971 American Mathematical Society