Two theorems of Efremovič in pointfree context (Q1304905)

For uniform frames the author proves analogues of the following two (related) classical results on uniformities: If two uniformities on the same set, with countable bases, have the same Samuel compactification, then they are equal; furthermore, every proximal map from a metric space to a uniform space is uniformly continuous. Indeed, by making use of his approach to uniform frames via Weil entourages, he shows that if two uniformities of countable type on the same frame have the same totally bounded coreflection, then they are equal, and that every proximal homomorphism from a uniform frame to a uniform frame of countable type is uniform.