An approximation theorem for non-decreasing functions on compact posets

TL;DR

This paper proves a Stone-Weierstrass type approximation theorem for non-decreasing continuous functions defined on compact partially ordered sets, extending classical approximation results to ordered topological spaces.

Contribution

It introduces a new approximation theorem specifically for non-decreasing functions on compact posets, broadening the scope of classical theorems.

Findings

Establishes a Stone-Weierstrass type theorem for non-decreasing functions

Extends approximation theory to functions on compact posets

Provides a foundation for further research in ordered topological spaces

Abstract

In this short note we prove a theorem of the Stone-Weierstrass sort for subsets of the cone of non-decreasing continuous functions on compact partially ordered sets.