Lattices of uniformly continuous functions determine their sublattices of bounded functions

Abstract

If two uniform spaces have isomorphic lattices of their uniformly continuous real-valued functions then also their sublattices of bounded functions are isomorphic. That result is used to give a different correct proof of Shirota theorem (complete metric spaces are determined by their uniformly continuous real-valued functions) than that in [1].

Keywords

• Lattice of functions
• Uniform continuity