Necessity of non-stratified and anti-stratified spaces in lattice-valued topology
type: Item
instance of: scholarly article
title: Necessity of non-stratified and anti-stratified spaces in lattice-valued topology
zbMATH Open document ID: 1194.54011
published in: Fuzzy Sets and Systems
publication date: 2010-05-07T00:00:00Z
review text: The necessity of stratified spaces in lattice-valued topology is well known. On the other hand, the necessity of non-stratified spaces was recognized a long time ago. The paper provides some further arguments for the necessity of both stratified and non-stratified spaces in fixed-basis topology and variable-basis topology. This is done by studying the characteristic functor, the \(L\)-spectrum and \(L\)-soberification functors, the upper free functor associated with chain-valued frames, and two functorial embeddings associated with topological systems from semantic domains.
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 5705400
zbMATH Keywords: \(L\)-top
zbMATH Keywords: fixed-basis topology
zbMATH Keywords: loc-top
zbMATH Keywords: variable-basis topology
zbMATH Keywords: \(L\)-frame
zbMATH Keywords: \(L\)-locale
zbMATH Keywords: \(L\)-frm
zbMATH Keywords: \(L\)-loc
zbMATH Keywords: non-stratified \(L\)-topological space
zbMATH Keywords: anti-stratified \(L\)-topological space
zbMATH Keywords: normalized \(L\)-topological space
zbMATH Keywords: conormalized \(L\)-topological space
zbMATH Keywords: binormalized \(L\)-topological space
zbMATH Keywords: hypernormalized \(L\)-topological space
zbMATH Keywords: \(L\)-sobriety
zbMATH Keywords: \(L\)-spectrum
zbMATH Keywords: satisfaction relation
zbMATH Keywords: topological system
zbMATH Keywords: topsys
author: S. E. Rodabaugh
reviewed by: Javier Gutiérrez García
MaRDI profile type: Publication
full work available at URL: j.fss.2009.11.010
OpenAlex ID: W2069508716
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DOI: 10.1016/J.FSS.2009.11.010
description: scientific article; zbMATH DE number 5705400