Functional Analysis and Its Applications

, Volume 46, Issue 1, pp 69–72 | Cite as

Roundings in partially ordered topological spaces

  • A. L. Kryukova
Brief Communications


We obtain criteria for equivalence, covariance, commutativity, and idempotent additivity of roundings in ordered topological spaces. For some special classes of spaces, we obtain the characterization of roundings as extreme points of the set of nonenlarging isotone mappings and prove their Hyers-Ulam stability. A functional model of interval rounding is constructed.

Key words

Rounding partially ordered topological space extreme point Hyers-Ulam stability 


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  1. [1]
    G. Birkhoff, Lattice Theory, Amer. Math. Soc., New York, 1948.MATHGoogle Scholar
  2. [2]
    T. E. Kaminsky and V. Kreinovich, Notes on Intuitionistic Fuzzy Sets (NIFS), 4:3 (1998), 57–64.Google Scholar
  3. [3]
    T. E. Kaminsky, in: Studies on Mathematical Analysis and Mathematics Teaching Methodology [in Russian], Rus’, Vologda, 2000, 23–36.Google Scholar
  4. [4]
    U. Kulisch, Numer. Math., 18:1 (1971), 1–17.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    G. L. Litvinov, The Maslov dequantization, idempotent and tropical mathematics: A brief introduction,
  6. [6]
    E. V. Shulman, J. London Math. Soc. (2), 54:1 (1996), 111–120.MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Vologda State Pedagogical UniversityVologdaRussia

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