An extension of Morita’s metrization theorem
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- by Charles C. Alexander PDF
- Proc. Amer. Math. Soc. 30 (1971), 578-582 Request permission
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.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- 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