Characterizations of inductive posets with applications

Tasković, Milan R.

doi:10.1090/S0002-9939-1988-0962843-X

Characterizations of inductive posets with applications
HTML articles powered by AMS MathViewer

by Milan R. Tasković PDF

Proc. Amer. Math. Soc. 104 (1988), 650-659 Request permission

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.

References

Smbat Abian and Arthur B. Brown, A theorem on partially ordered sets, with applications to fixed point theorems, Canadian J. Math. 13 (1961), 78–82. MR 123492, DOI 10.4153/CJM-1961-007-5
Kenneth Baclawski and Anders Björner, Fixed points in partially ordered sets, Adv. in Math. 31 (1979), no. 3, 263–287. MR 532835, DOI 10.1016/0001-8708(79)90045-8
Garrett Birkhoff, Lattice Theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. 25, American Mathematical Society, New York, N. Y., 1948. MR 0029876
Nicolas Bourbaki, Sur le théorème de Zorn, Arch. Math. (Basel) 2 (1949/50), 434–437 (1951) (French). MR 47739, DOI 10.1007/BF02036949
Anne C. Davis, A characterization of complete lattices, Pacific J. Math. 5 (1955), 311–319. MR 74377, DOI 10.2140/pjm.1955.5.311
Hartmut Höft and Margret Höft, Some fixed point theorems for partially ordered sets, Canadian J. Math. 28 (1976), no. 5, 992–997. MR 419306, DOI 10.4153/CJM-1976-097-0

Fixed edge theorems for complete lattices

17

Jiří Klimeš, Fixed point characterization of completeness on lattices for relatively isotone mappings, Arch. Math. (Brno) 20 (1984), no. 3, 125–132. MR 784863
Đuro Kurepa, Fixpoints of decreasing mappings of ordered sets, Publ. Inst. Math. (N.S.) 18(32) (1975), 111–116. MR 0369189
George Markowsky, Chain-complete posets and directed sets with applications, Algebra Universalis 6 (1976), no. 1, 53–68. MR 398913, DOI 10.1007/BF02485815
T. B. Muenzenberger and R. E. Smithson, Characterizations of compactness of the interval topology in semilattices, Proc. Amer. Math. Soc. 46 (1974), 133–136. MR 345885, DOI 10.1090/S0002-9939-1974-0345885-7
S. R. Kogalovskiĭ, On a theorem of Frink, Uspehi Mat. Nauk 19 (1964), no. 2 (116), 143–145 (Russian). MR 0161808
Ivan Rival, A fixed point theorem for finite partially ordered sets, J. Combinatorial Theory Ser. A 21 (1976), no. 3, 309–318. MR 419308, DOI 10.1016/0097-3165(76)90003-0
R. E. Smithson, Fixed points in partially ordered sets, Pacific J. Math. 45 (1973), 363–367. MR 316323, DOI 10.2140/pjm.1973.45.363
Alfred Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math. 5 (1955), 285–309. MR 74376, DOI 10.2140/pjm.1955.5.285

Banach’s mappings of fixed points on spaces and ordered sets

8

M. R. Tasković, A monotone principle of fixed points, Proc. Amer. Math. Soc. 94 (1985), no. 3, 427–432. MR 787887, DOI 10.1090/S0002-9939-1985-0787887-X
Milan R. Tasković, On an equivalent of the axiom of choice and its applications, Math. Japon. 31 (1986), no. 6, 979–991. MR 870984
L. E. Ward Jr., Completeness in semi-lattices, Canadian J. Math. 9 (1957), 578–582. MR 91264, DOI 10.4153/CJM-1957-065-3
E. S. Wolk, Dedekind completeness and a fixed-point theorem, Canadian J. Math. 9 (1957), 400–405. MR 86788, DOI 10.4153/CJM-1957-047-5

Neuer Beweis für die Möglichkeit einer Wohlordnung

15