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Article

Bhatta, S. Parameshwara
Weak chain-completeness and fixed point property for pseudo-ordered sets. (English). Czechoslovak Mathematical Journal, vol. 55 (2005), issue 2, pp. 365-369
MSC: 06B05 | MR 2137143 | Zbl 1081.06004
Keywords:
pseudo-ordered set; trellis; complete trellis; fixed point property; weak chain completeness
Summary:
In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point.
References:
[1] P. Crawley and R. P. Dilworth: Algebraic Theory of Lattices. Prentice-Hall, Englewood Cliffs, 1973.
[2] J. Lewin: A simple proof of Zorn’s lemma. Amer. Math. Monthly 98 (1991), 353–354. DOI 10.2307/2323807 | MR 1103192 | Zbl 0749.04002
[3] G. Markowski: Chain-complete posets and directed sets with applications. Algebra Universalis 6 (1976), 54–69. MR 0398913
[4] H. L. Skala: Trellis theory. Algebra Universalis 1 (1971), 218–233. DOI 10.1007/BF02944982 | MR 0302523 | Zbl 0242.06003
[5] H. Skala: Trellis Theory. Mem. Amer. Math. Soc. 121, Providence, 1972. MR 0325474 | Zbl 0242.06004
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