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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniformly convex totally ordered sets
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by R. H. Redfield PDF
Proc. Amer. Math. Soc. 51 (1975), 289-294 Request permission

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
  • Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
  • 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.
  • Leopoldo Nachbin, Topology and order, Van Nostrand Mathematical Studies, No. 4, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1965. Translated from the Portuguese by Lulu Bechtolsheim. MR 0219042
  • R. H. Redfield, Ordering uniform completions of partially ordered sets, Canadian J. Math. 26 (1974), 644–664. MR 362251, DOI 10.4153/CJM-1974-062-4
  • R. H. Redfield, Ordering uniform completions of partially ordered sets, Proceedings of the University of Houston Lattice Theory Conference (Houston, Tex., 1973) Dept. Math., Univ. Houston, Houston, Tex., 1973, pp. 504–511. MR 0394594
  • Wolfgang J. Thron, Topological structures, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR 0200892
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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