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.
For ordered (= partially ordered) sets we introduce certain cardinal characteristics of them (some of those are known). We show that these characteristics—with one exception—coincide.