The Katětov-Morita theorem for the dimension of metric frames
type: Item
instance of: scholarly article
title: The Katětov-Morita theorem for the dimension of metric frames
zbMATH Open document ID: 1208.06004
author: D. Brijlall
author: Dharmanand Baboolal
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2010-10-01T00:00:00Z
review text: This paper is an interesting contribution to the dimension theory of metric frames. In it, after characterizing the dimension \(\dim\) of metric frames in terms of special sequences of covers, the authors prove the point-free counterpart of the classical Katětov-Morita Theorem for metric spaces asserting that \(\operatorname{Ind}L=\dim L\) for every metric frame \(L\). Then, among other results, they prove that for every separable metric frame \(L\), \(\operatorname{Ind}L= \operatorname{Ind}L= \dim L\). A note of caution to the reader: there are a few mistakes in the numbering of results in Section~5.
reviewed by: Jorge Picado
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54F45
zbMATH DE Number: 5794226
zbMATH Keywords: metric frame
zbMATH Keywords: metric locale
zbMATH Keywords: dimension functions
zbMATH Keywords: covering dimension
zbMATH Keywords: Menger-Urysohn dimension
zbMATH Keywords: Brouwer-Čech dimension
MaRDI profile type: Publication
full work available at URL: s13226-010-0025-x
OpenAlex ID: W2002547765
cites work: Some aspects of dimension theory of frames
cites work: Stone-čech Compactification and Dimension Theory for Regular σ-Frames
cites work: Q4087970
cites work: SEPARABILITY IN LOCALES
cites work: On point-finiteness in pointfree topology
cites work: Q3218788
cites work: Quotient maps of locales
cites work: Categories of diametric frames
cites work: Q3820654
DOI: 10.1007/S13226-010-0025-X
description: scientific article; zbMATH DE number 5794226