SPREAD UNIFORMITIES AND UNIFORM SPREADS

Abstract

We discuss a point-free analog of the topological fact that every uniformly continuous function on a dense subspace of a uniform space into a complete uniform space has a unique uniformly continuous extension. It is shown that a uniform frame homomorphism h: L → M from a complete uniform frame L into a uniform frame M (not necessarily complete) onto which a dense surjection p: N → M maps has a unique uniform extension g: L → N such that p o g = h. We introduce spread uniformities and uniform spreads into the theory of uniform frames, and, then, show that the extension so constructed is a uniform spread.