Approximations for uniformly continuous functions on groupoids

Abstract

The purpose of this paper is to prove an approximation/extension theorem for a family of partial functions on a groupoid satisfying a uniform compatibility condition. In the particular case of a trivial groupoid G=X× X and a singleton family, we recover the well-known result of Katětov: every bounded uniformly continuous real-valued function f defined on a subspace of a uniform space X has a bounded uniformly continuous extension to X.

Keywords

• groupoid
• uniformity
• extension theorem