A characterization of inductive posets
Jiří Klimeš (1985)
Archivum Mathematicum
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Jiří Klimeš (1985)
Archivum Mathematicum
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Heikkilä, S. (2010)
Fixed Point Theory and Applications [electronic only]
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S. Parameshwara Bhatta (2005)
Czechoslovak Mathematical Journal
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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.
Vítězslav Novák, Tomáš Novotný (2005)
Discussiones Mathematicae - General Algebra and Applications
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Continuity of isotone mappings and embeddings of a chain G into another chain are studied. Especially, conditions are found under which the set of points of discontinuity of such a mapping is dense in G.
Radomír Halaš, Daniel Hort (2003)
Czechoslovak Mathematical Journal
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We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.