Metric and symmetric spaces
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- by Peter W. Harley PDF
- Proc. Amer. Math. Soc. 43 (1974), 428-430 Request permission
Abstract:
In this paper we give an alternative proof, without reference to Urysohn’s lemma, of the metrization theorem of Bing [2], Nagata [6], and Smirnov [8] via the theory of symmetric spaces as developed by H. Martin in [5].References
- A. V. Arhangel′skiĭ, Mappings and spaces, Russian Math. Surveys 21 (1966), no. 4, 115–162. MR 0227950, DOI 10.1070/RM1966v021n04ABEH004169
- R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175–186. MR 43449, DOI 10.4153/cjm-1951-022-3
- A. H. Frink, Distance functions and the metrization problem, Bull. Amer. Math. Soc. 43 (1937), no. 2, 133–142. MR 1563501, DOI 10.1090/S0002-9904-1937-06509-8
- Kiiti Morita and Sitiro Hanai, Closed mappings and metric spaces, Proc. Japan Acad. 32 (1956), 10–14. MR 87077
- Harold W. Martin, Metrization of symmetric spaces and regular maps, Proc. Amer. Math. Soc. 35 (1972), 269–274. MR 303511, DOI 10.1090/S0002-9939-1972-0303511-5
- Jun-iti Nagata, On a necessary and sufficient condition of metrizability, J. Inst. Polytech. Osaka City Univ. Ser. A 1 (1950), 93–100. MR 43448
- Dale Rolfsen, Alternative metrization proofs, Canadian J. Math. 18 (1966), 750–757. MR 198427, DOI 10.4153/CJM-1966-075-9
- Yu. Smirnov, A necessary and sufficient condition for metrizability of a topological space, Doklady Akad. Nauk SSSR (N.S.) 77 (1951), 197–200 (Russian). MR 0041420
- A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690–700. MR 87078, DOI 10.1090/S0002-9939-1956-0087078-6
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 428-430
- MSC: Primary 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1974-0336713-4
- MathSciNet review: 0336713