Displaying similar documents to “Ordering the set of antichains of an ordered set.”

Characterizations of totally ordered sets by their various endomorphisms

Daniel Hort, Jan Chvalina, Jiří Moučka (2002)

Czechoslovak Mathematical Journal

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We characterize totally ordered sets within the class of all ordered sets containing at least three-element chains using a simple relationship between their isotone transformations and the so called 2-, 3-, 4-endomorphisms which are introduced in the paper. Another characterization of totally ordered sets within the class of ordered sets of a locally finite height with at least four-element chains in terms of the regular semigroup theory is also given.