Displaying similar documents to “Properties of monotone mappings in partially ordered sets.”

A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets

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.

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.