The general fuzzy filter approach to fuzzy topology. II
type: Item
instance of: scholarly article
title: The general fuzzy filter approach to fuzzy topology. II
zbMATH Open document ID: 0873.54009
DOI: 10.1016/0165-0114(95)00057-R
author: Werner Gähler
published in: Fuzzy Sets and Systems
publication date: 1997-10-29T00:00:00Z
review text: By means of the notion of fuzzy filter developed in Part I [ibid. 205-224 (1995; Zbl 0873.54008), see the review above], here the author characterizes fuzzy topologies by interior operators, fuzzy neighborhoods, fuzzy neighborhood filters, fuzzy neighborhood operators, open fuzzy filters, interior fuzzy filter operators \(\dots\) (the fuzzy topologies can be identified with the monadic topologies with respect to the partially ordered fuzzy filter monad). Further notions for fuzzy filters treated here are trace, inner and adherence point, projective openness and closeness, closure operator, compactness; usual properties of subsets, continuous functions and products are shown to be valid. Previous results on stratified fuzzy topologies (all constant fuzzy sets are open) are included in a natural manner as special cases.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 18C15
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 919471
zbMATH Keywords: fuzzy neighborhood
zbMATH Keywords: monadic topologies
zbMATH Keywords: partially ordered fuzzy filter monad
reviewed by: Bernhard Behrens
MaRDI profile type: Publication
cites work: Fuzzy topological spaces
cites work: Q4010276
cites work: Q4280785
cites work: Q4280788
cites work: L-fuzzy sets
cites work: Convergence in fuzzy topological spaces
cites work: Q4215784
cites work: Fuzzy topology. I: Neighborhood structure of a fuzzy point and Moore-Smith convergence
full work available at URL: 0165-0114(95)00057-r
OpenAlex ID: W2058200197
description: scientific article; zbMATH DE number 919471