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)

 
 

 

Uniformly convex totally ordered sets


Author: R. H. Redfield
Journal: Proc. Amer. Math. Soc. 51 (1975), 289-294
MSC: Primary 54F05; Secondary 06A45
DOI: https://doi.org/10.1090/S0002-9939-1975-0394595-X
MathSciNet review: 0394595
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Since a uniformly convex totally ordered set is a uniform lattice, its uniform completion is totally ordered in a natural way. The assumption of uniform convexity is a small restriction because every nearly uniform ordered space is uniformly convex.


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

  • [1] G. Birkhoff, Lattice theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1967. MR 37 #2638. MR 0227053 (37:2638)
  • [2] N. Bourbaki, Eléements de mathématique. I: Les structures fondamentales de l'analyse. Livre III: Topologie générale, Actualités Sci. Indust., nos. 1029, 1045, 1084, 1142, 1143, Hermann, Paris, 1947, 1948, 1949; English transl., Hermann, Paris; Addison-Wesley, Reading, Mass., 1966. MR 34 # 5044b.
  • [3] L. Nachbin, Topology and order, Van Nostrand Math. Studies, no. 4, Van Nostrand, Princeton, N. J., 1965. MR 36 #2125. MR 0219042 (36:2125)
  • [4] R. H. Redfield, Ordering uniform completions of partially ordered sets, Canad. J. Math. 26 (1974), 644-664. MR 0362251 (50:14693)
  • [5] -, Ordering uniform completions of partially ordered sets, Lattice Theory, Proc. University of Houston Conf., Math. Dept., Univ. of Houston, Houston, Tex., 1974, pp. 504-511. MR 0394594 (52:15395)
  • [6] W. Thron, Topological structures, Holt, Rinehart and Winston, New York, 1966. MR 34 #778. MR 0200892 (34:778)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F05, 06A45

Retrieve articles in all journals with MSC: 54F05, 06A45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0394595-X
Keywords: Uniform ordered space, totally ordered set, uniform completion, uniform lattice, uniformly convex
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society