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

Radomír Halaš;  Daniel Hort — 2003

Czechoslovak Mathematical Journal

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

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.

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