Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Metric and symmetric spaces


Author: Peter W. Harley
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] A. V. Arhangel'skiĭ, Mappings and spaces, Uspehi Mat. Nauk 21 (1966), no. 4 (130), 133-184 = Russian Math. Surveys 21 (1966), no. 4, 115-162. MR 37 #3534. MR 0227950 (37:3534)
  • [2] R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175-186. MR 13, 264. MR 0043449 (13:264f)
  • [3] A. H. Frink, Distance functions and the metrization problem, Bull. Amer. Math. Soc. 43 (1937), 133-142. MR 1563501
  • [4] S. Hanai and K. Morita, Closed mappings and metric spaces, Proc. Japan. Acad. 32 (1956), 10-14. MR 19, 299. MR 0087077 (19:299a)
  • [5] H. W. Martin, Metrization of symmetric spaces and regular maps, Proc. Amer. Math. Soc. 35 (1972), 269-274. MR 0303511 (46:2648)
  • [6] J. Nagata, On a necessary and sufficient condition for metrizability, J. Inst. Polytech. Osaka City Univ. Ser. A Math. 1 (1950), 93-100. MR 13, 264. MR 0043448 (13:264e)
  • [7] D. Rolfsen, Alternative metrization proofs, Canad. J. Math. 18 (1966), 750-757. MR 33 #6585. MR 0198427 (33:6585)
  • [8] Ju. M. Smirnov, A necessary and sufficient condition for metrizability of a topological space, Dokl. Akad. Nauk SSSR (N.S.) 77 (1951), 197-200. (Russian) MR 12, 845. MR 0041420 (12:845c)
  • [9] A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690-700. MR 19, 299. MR 0087078 (19:299b)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54E35

Retrieve articles in all journals with MSC: 54E35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0336713-4
Keywords: Metrizable space, symmetrizable space, $ \sigma $-locally finite base
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society