The gauge of a uniform frame
type: Item
instance of: scholarly article
title: The gauge of a uniform frame
zbMATH Open document ID: 1022.06004
DOI: 10.1023/A:1020983200712
author: Jorge Picado
published in: Applied Categorical Structures
publication date: 2003-04-03T00:00:00Z
review text: The author characterizes gauge structures for frames, i.e., families of metric diameters which describe frame uniformities. The main purpose of this paper is to present a characterization of frame uniformities that is analogous to the spatial one given in terms of pseudometrics. The author investigates frame uniformities in the sense of Bourbaki and proves the following theorem: There is a one-one correspondence between the class of uniformities on a frame \(L\) and the class of gauge structures on \(L\). Finally, he gives some correspondences: gauge structures make clear the nature of the generalization from metric frames to uniform frames and, moreover, metric frames generate all gauge frames, in the sense that each gauge frame is a quotient of a coproduct of metric frames.
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 1892224
zbMATH Keywords: gauge structures
zbMATH Keywords: metric diameters
zbMATH Keywords: frame uniformities
zbMATH Keywords: uniform frames
zbMATH Keywords: metric frames
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
full work available at URL: a:1020983200712
OpenAlex ID: W1590544422
description: scientific article; zbMATH DE number 1892224