Geodesic
Roundings in Partially Ordered Topological Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 83-87 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: rounding, partially ordered topological space, extreme point, Hyers–Ulam stability. 
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A. L. Kryukova. Roundings in Partially Ordered Topological Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 83-87. http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a9/

[1] G. Birkgof, Teoriya struktur, IL, M., 1952

[2] T. E. Kaminsky, V. Kreinovich, Notes on intuitionistic fuzzy sets, 4:3 (1998), 57–64 | MR

[3] T. E. Kaminskii, Issledovaniya po matematicheskomu analizu i metodike prepodavaniya matematiki, Rus, Vologda, 2000, 23–36

[4] U. Kulisch, Numer. Math., 18:1 (1971), 1–17 | DOI | MR | Zbl

[5] G. L. Litvinov, The Maslov dequantization, idempotent and tropical mathematics: A brief introduction, arXiv: math/0507014v1

[6] E. V. Shulman, J. London Math. Soc. (2), 54:1 (1996), 111–120 | DOI | MR | Zbl