Weak chain-completeness and fixed point property for pseudo-ordered sets. (English) Zbl 1081.06004

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.


06B05 Structure theory of lattices
06A75 Generalizations of ordered sets


Zbl 0332.06001
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