Geodesic
Some Fixed Point Theorems for Partially Ordered Sets
Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 992-997

Voir la notice de l'article provenant de la source Cambridge University Press

A partially ordered set P has the fixed point property if every order-preserving map f : P → P has a fixed point, i.e. there exists x ∊ P such that f(x) = x. A. Tarski's classical result (see [4]), that every complete lattice has the fixed point property, is based on the following two properties of a complete lattice P: (A) For every order-preserving map f : P → P there exists x ∊ P such that x ≦ f(x). (B) Suprema of subsets of P exist; in particular, the supremum of the set {x|x ≦ f(x)} ⊂ P exists. 
Höft, Hartmut; Höft, Margret. Some Fixed Point Theorems for Partially Ordered Sets. Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 992-997. doi: 10.4153/CJM-1976-097-0
@article{10_4153_CJM_1976_097_0,
     author = {H\"oft, Hartmut and H\"oft, Margret},
     title = {Some {Fixed} {Point} {Theorems} for {Partially} {Ordered} {Sets}},
     journal = {Canadian journal of mathematics},
     pages = {992--997},
     year = {1976},
     volume = {28},
     number = {5},
     doi = {10.4153/CJM-1976-097-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-097-0/}
}
TY  - JOUR
AU  - Höft, Hartmut
AU  - Höft, Margret
TI  - Some Fixed Point Theorems for Partially Ordered Sets
JO  - Canadian journal of mathematics
PY  - 1976
SP  - 992
EP  - 997
VL  - 28
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-097-0/
DO  - 10.4153/CJM-1976-097-0
ID  - 10_4153_CJM_1976_097_0
ER  - 
%0 Journal Article
%A Höft, Hartmut
%A Höft, Margret
%T Some Fixed Point Theorems for Partially Ordered Sets
%J Canadian journal of mathematics
%D 1976
%P 992-997
%V 28
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-097-0/
%R 10.4153/CJM-1976-097-0
%F 10_4153_CJM_1976_097_0

[1] 1. Abian, S. and Brown, A. B., A theorem on partially ordered sets, with applications to fixed point theorems, Can. J. Math. 13 (1961), 78–82. Google Scholar

[2] 2. Birkhoff, G., Lattice theory, 3rd edition (AMS Coll. Pub. XXV, 1973) Google Scholar

[3] 3. Rival, I., A fixed point theorem for finite partially ordered sets, Preprint Nr. 184, Januar 1975, Technische Hochschule Darmstadt. Google Scholar

[4] 4. Tarski, A., A lattice-theoreticalfixpoint theorem and its applications, Pacific J. Math. 5 (1955), 285–309. Google Scholar

[5] 5. Wong, J. S. W., Common fixed points of commuting monotone mappings, Can. J. Math. 19 (1967), 617–620. Google Scholar

Cité par Sources :