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Characterizations of inductive posets with applications


Author: Milan R. Tasković
Journal: Proc. Amer. Math. Soc. 104 (1988), 650-659
MSC: Primary 06A10
DOI: https://doi.org/10.1090/S0002-9939-1988-0962843-X
MathSciNet review: 962843
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Abstract: This paper presents new characterizations of inductiveness of posets in terms of fixed apexes and fixed points. Applications in nonlinear functional analysis and fixed point theory are considered.


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  • [AB] S. Abian and A. Brown, A theorem on partially ordered sets with application to fixed point theorems, Canad. J. Math. 13 (1961), 78-83. MR 0123492 (23:A817)
  • [BB] K. Baclawski and A. Björner, Fixed points in partially ordered sets, Adv. in Math. 31 (1979), 263-287. MR 532835 (81c:06001)
  • [BG] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1948. MR 0029876 (10:673a)
  • [BO] N. Bourbaki, Sur le théorème de Zorn, Arch. Math. 2 (1950), 434-437. MR 0047739 (13:923j)
  • [DA] A. Davis, A characterization of complete lattices, Pacific J. Math. 5 (1955), 311-319. MR 0074377 (17:574e)
  • [HH] H. Höft and M. Höft, Some fixed point theorems for partially ordered sets, Canad. J. Math. 28 (1976), 992-997. MR 0419306 (54:7328)
  • [KJ] J. Klimeš, Fixed edge theorems for complete lattices, Arch. Math. 17 (1981), 227-234.
  • [KL] -, Fixed points characterization of completeness of lattice for relatively isotone mappings, Arch. Math. 3 20 (1984), 125-132. MR 784863 (86m:06004)
  • [KD] Dj. Kurepa, Fixpoints of decreasing mappings of ordered sets, Publ. Inst. Math. 32 (1975), 111-116. MR 0369189 (51:5424)
  • [MG] G. Markovski, Chain-complete posets and directed sets with applications, Algebra Universalis 6 (1976), 53-68. MR 0398913 (53:2764)
  • [MS] B. Muenzenberger and E. Smithson, Characterizations of compactness of the interval topology in semilattices, Proc. Amer. Math. Soc. 46 (1974), 133-136. MR 0345885 (49:10615)
  • [KO] S. Kogalovskij, On a theorem of Frink, Uspekhi Math. Nauk 19 (1964), 143-145. MR 0161808 (28:5012)
  • [RI] I. Rival, A fixed point theorem for finite partially ordered sets, J. Combin. Theory A21 (1976), 309-318. MR 0419308 (54:7330)
  • [SR] R. E. Smithson, Fixed points in partially ordered sets, Pacific J. Math. 45 (1973), 363-367. MR 0316323 (47:4871)
  • [TA] A. Tarski, A lattice theoretical fixed point theorem and its applications, Pacific J. Math. 5 (1955), 285-309. MR 0074376 (17:574d)
  • [TM] M. Tasković, Banach's mappings of fixed points on spaces and ordered sets (These), Math. Balkanica 8 (1978), 150.
  • [MT] -, A monotone principle of fixed points, Proc. Amer. Math. Soc. 94 (1985), 427-432. MR 787887 (87c:54065)
  • [TAS] -, On an equivalent of the axiom of choice and its applications, Math. Japon. 31 (1986), 979-991. MR 870984 (88a:04002)
  • [WA] E. Ward, Completeness in semi-lattices, Canad. J. Math. 9 (1957), 578-582. MR 0091264 (19:938a)
  • [WO] S. Wolk, Dedekind completeness and a fixed point theorem, Canad. J. Math. 9 (1957), 400-405. MR 0086788 (19:243d)
  • [ZE] E. Zermelo, Neuer Beweis für die Möglichkeit einer Wohlordnung, Math. Ann. 15 (1908), 107-128.

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DOI: https://doi.org/10.1090/S0002-9939-1988-0962843-X
Article copyright: © Copyright 1988 American Mathematical Society

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