Abstract
The purpose of this paper is to introduce a class of mappings from a lattice L, whose elements are residuated maps, into itself. The main results of this paper identify certain injective residuated mappings of L and order automorphisms of a sublattice of L with mappings from this class.
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References
F.Baulieu (1985) Order theoretic classification of montone equivariant cluster methods, Algebra Universalis 20, 351–367.
F. Baulieu (to appear) Classification of normalized cluster methods in an order theoretic model, Order.
G.Birkhoff (1967) Lattice Theory, 3rd edition, Amer. Math Soc., Providence.
T. S.Blyth and M. F.Janowitz (1972) Residuation Theory, Pergamon Press, London.
M. F.Janowitz (1978) An order theoretic model for cluster analysis, SIAM J. Appl. Math., 34, 55–72.
M. F.Janowitz and B.Schweizer (1989) Ordinal and percentile clustering, Math. Social Sciences, 18, 135–186.
M.Loeve (1977) Probability Theory, Spinger-Verlag, New York.
D. G. Mowat (1968) Ph.D. Thesis, University of Waterloo.
R. C.Powers, (1988) Order automorphisms of spaces of nondecreasing functions, J. Math. Anal. Appl. 136, 112–123.
R. C. Powers (submitted) (1989) Flatness and continuity in the percentile model.
R. C. Powers (1988) Order theoretic classification of percentile cluster methods, Doctoral Dissertation, Univ. of Massachusetts, Amherst.
E. A. Schreiner (1973) Tight residuated mappings, Proc. Univ. of Houston Lattice Theory Conference, pp. 519–530.
B.Schweizer and A.Sklar (1983) Probabilistic Metric Spaces, Elsevier North-Holland Publ. Co., New York.
Z.Shmuely (1974) The structure of Galois connections, Pacific J. Math. 54, 209–225.
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Powers, R.C. Induced residuated maps. Order 7, 83–96 (1990). https://doi.org/10.1007/BF00383176
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DOI: https://doi.org/10.1007/BF00383176