Bhatta, S. Parameshwara Weak chain-completeness and fixed point property for pseudo-ordered sets. (English) Zbl 1081.06004 Czech. Math. J. 55, No. 2, 365-369 (2005). 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 G. Markowsky [Algebra Univers. 6, 53–68 (1976; Zbl 0332.06001)]), and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point. Cited in 1 ReviewCited in 2 Documents MSC: 06B05 Structure theory of lattices 06A75 Generalizations of ordered sets Keywords:pseudo-ordered set; trellis; complete trellis; fixed-point property; weak chain completeness Citations:Zbl 0332.06001 PDF BibTeX XML Cite \textit{S. P. Bhatta}, Czech. Math. J. 55, No. 2, 365--369 (2005; Zbl 1081.06004) Full Text: DOI EuDML Link OpenURL References: [1] P. Crawley and R. P. Dilworth: Algebraic Theory of Lattices. Prentice-Hall, Englewood Cliffs, 1973. · Zbl 0494.06001 [2] J. Lewin: A simple proof of Zorn’s lemma. Amer. Math. Monthly 98 (1991), 353–354. · Zbl 0749.04002 [3] G. Markowski: Chain-complete posets and directed sets with applications. Algebra Universalis 6 (1976), 54–69. [4] H. L. Skala: Trellis theory. Algebra Universalis 1 (1971), 218–233. · Zbl 0242.06003 [5] H. Skala: Trellis Theory. Mem. Amer. Math. Soc. 121, Providence, 1972. · Zbl 0242.06004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.