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A New Proof of Certain Metrization Theorems

Published online by Cambridge University Press:  20 November 2018

Marion B. Smith Jr.*
Affiliation:
University of Utah, University of Wisconsin
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A well-known problem in topology is the so-called metrization problem. This consists of asking for the topological conditions that are necessary and sufficient in order to guarantee that a topological space be metrizable. The first solution of this problem was given in 1923 by P. Alexandroff and P. Urysohn (1).

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Alexandroff, P. and Urysohn, P., Une condition nécessaire et suffisante pour qu'une classe (L) soit une classe (B), C. R. Acad. Se, 177 (1923), 12741276.Google Scholar
2. Bing, R. H., Extending a Metric, Duke Math. J., 14 (1947), 511519.Google Scholar
3. Bing, R. H., Metrization of topological spaces, Can. J. Math., 3 (1951), 175186.Google Scholar
4. Chittenden, E. W., On the equivalence of écart and voisinage, Trans. Amer. Math. Soc, 18 (1917), 161166.Google Scholar
5. Frink, A. H., Distance functions and the metrization problem, Bull. Amer. Math. Soc, 43 (1937), 133142.Google Scholar
6. Kelley, J. L., General topology (Princeton, 1955).Google Scholar
7. Nagata, J., On a necessary and sufficient condition of metrizability, J. Inst. Poly tech. Osaka City Univ., 1 (1950), 93100.Google Scholar
8. Ribeiro, H., Sur les espaces à métrique faible, Portugaliae Mathematica, 4 (1943), 2140.Google Scholar
9. Smirnov, Yu. M., A necessary and sufficient condition for metrizability of a topological space, Doklady Akad. Nauk. S.S.S.R., N.S., 77 (1951), 197200.Google Scholar
10. Weil, A., Sur les espaces à structure uniforme et sur la topologie générale, Actualités Sci. Ind., 551 (Paris, 1937).Google Scholar