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An Extension of Morita's Metrization Theorem
Charles C. Alexander
Proceedings of the American Mathematical Society
Vol. 30, No. 3 (Nov., 1971), pp. 578-582
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2037738
Page Count: 5
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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.
Proceedings of the American Mathematical Society © 1971 American Mathematical Society