On characterizing Riesz spaces C(X) without Yosida representation

Abstract

We characterize Riesz spaces C(X) of real-valued continuous functions on a topological (Tychonoff) space X without using the Yosida representation theorem. The approach is elementary by using a simple description of zero-sets and a kind of local uniform completeness avoiding inversion closeness.

Keywords

• Archimedean Riesz space
• Locally uniformly complete
• Real-valued continuous functions
• Weak order unit
• Zero-separation