An insertion theorem for continuous \(\mathbb I(L)\)-valued functions and its consequences
type: Item
instance of: scholarly article
title: An insertion theorem for continuous \(\mathbb I(L)\)-valued functions and its consequences
zbMATH Open document ID: 1058.54005
DOI: 10.1016/S0165-0114(03)00300-2
author: Iraide Mardones-Pérez
author: Tomasz Kubiak
published in: Fuzzy Sets and Systems
publication date: 2004-08-20T00:00:00Z
review text: The work deals with a generalisation of the insertion theorem, i.e. the problem of inserting a continuous function between two comparable functions. The direction of the generalisation is from the two-point lattice \(\{ 0, 1\}\) to an arbitrary complete lattice \((L,')\) or, more precisely, from \({\mathbb{I}}(\{ 0,1\})\) to Hutton's \(L\)-interval \(\mathbb I(L)\). The results achieved for the insertion problem lead to consequences for a relation between complete regularity in the categories of \(L\)-topological and \(\mathbb I(L)\)-topological spaces with \(L\) a frame.
reviewed by: Vladimír Janiš
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54C05
zbMATH DE Number: 2093605
zbMATH Keywords: \(L\)-interval
zbMATH Keywords: insertion
zbMATH Keywords: complete L-regularity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2093605