Closure operators and lattice extensions
type: Item
instance of: scholarly article
title: Closure operators and lattice extensions
zbMATH Open document ID: 1060.06009
author: J. B. Nation
published in: Order
publication date: 2005-02-25T00:00:00Z
review text: Let \(\Gamma \) be a closure operator on a set \(X\). Then Cl\((X,\Gamma )\) denotes the lattice of \(\Gamma \)-closed subsets of \(X\). If \(\Gamma \) and \(\Delta \) are closure operators on the same set \(X\), then \(\Delta \) is a weak (resp. strong) extension of \(\Gamma \) if Cl\((X,\Gamma )\) is a complete meet-subsemilattice (resp. complete sublattice) of Cl\((X,\Delta )\). The paper deals with such extensions on finite lattices.
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06A15
zbMATH DE Number: 2138855
zbMATH Keywords: closure operator
zbMATH Keywords: congruence-preserving
zbMATH Keywords: extensions on finite lattices
reviewed by: Jiří Rachůnek
MaRDI profile type: Publication
full work available at URL: s11083-004-5178-y
OpenAlex ID: W2076513482
Wikidata QID: Q44884377
cites work: Largest extension of a finite convex geometry
cites work: Lattices with unique irreducible decompositions
cites work: Meet-distributive lattices and the anti-exchange closure
cites work: The theory of convex geometries
DOI: 10.1007/S11083-004-5178-Y
description: scientific article; zbMATH DE number 2138855