An isotonic mapping is a function between two partially ordered sets that preserves the ordering between the elements. Specifically, given two partially ordered sets $(X,\le)$ and $(Y,\le)$, a function $f:X\to Y$ is isotonic if for any $x, y\in X$ such that $x\le y$, it is true that $f(x) \le f(y)$.


I am looking for literature recommendations on classical and generalized isotonic mappings of sets. Specifically, I am interested in any scientific and technical literature on this topic that is available in English or Russian (other languages are also acceptable). I am open to both books and articles.

If anyone is knowledgeable in this area, could you suggest where this theory is actively used? Specifically, I am interested in learning about the specific areas of mathematics and algorithms that this theory is used in.

Thank you in advance for any help you can provide.