\(E\)-compactness in pointfree topology
type: Item
instance of: scholarly article
title: \(E\)-compactness in pointfree topology
zbMATH Open document ID: 1029.06006
DOI: 10.1023/A:1023597003585
author: Nizar Marcus
published in: Applied Categorical Structures
publication date: 2003-07-01T00:00:00Z
review text: The author presents a pointfree analogue of \(E\)-compactness as introduced by Engelking and Mrowka. Main results: 1. Let \(E\) be a regular frame, and \(L\) an \(E\)-regular frame. Then the following are equivalent: (1) \(L\) is \(E\)-complete. (2) \(L\) is a closed quotient of a copower of \(E\). (3) Every \(C_E\)-extension of \(L\) is an isomorphism. 2. The category of all \(E\)-compact frames is coreflective in the category of all \(E\)-regular frames. 3. The spatial \(E\)-compact frames are precisely those frames that are spatial reflections of \(E\)-complete frames. 4. The category of \(E\)-compact frames is closed under coproducts and closed quotients.
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54E17
zbMATH DE Number: 1944935
zbMATH Keywords: frames
zbMATH Keywords: nearness frames
zbMATH Keywords: relatively spatial reflections
zbMATH Keywords: \(E\)-complete frames
zbMATH Keywords: \(E\)-compact frames
zbMATH Keywords: Cauchy completeness
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
full work available at URL: a:1023597003585
OpenAlex ID: W1516176860
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description: scientific article; zbMATH DE number 1944935