Two theorems of Efremovič in pointfree context
type: Item
instance of: scholarly article
title: Two theorems of Efremovič in pointfree context
zbMATH Open document ID: 0929.54017
DOI: 10.1016/S0022-4049(98)00038-3
author: Jorge Picado
published in: Journal of Pure and Applied Algebra
publication date: 2000-01-23T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 54E05
zbMATH DE Number: 1340440
zbMATH Keywords: pointfree topology
zbMATH Keywords: proximal map
zbMATH Keywords: metrizable uniformity
zbMATH Keywords: uniform frames
zbMATH Keywords: Samuel compactification
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
full work available at URL: s0022-4049(98)00038-3
OpenAlex ID: W2093501533
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description: scientific article; zbMATH DE number 1340440