On fuzzy subspaces
type: Item
instance of: scholarly article
title: On fuzzy subspaces
zbMATH Open document ID: 0814.54003
DOI: 10.1016/0165-0114(93)90510-O
published in: Fuzzy Sets and Systems
publication date: 1994-04-17T00:00:00Z
review text: The authors suggest fuzzy topological subspaces of a fuzzy topological space as structures induced over each fuzzy subset from the fuzzy topology; they define the concept of fuzzy topological subspace as follows: ``Let \((X,\delta)\) be a fuzzy topological space and \(\mu \in I^ X\), then the family \(\delta_ \mu = \{\nu\wedge\mu:\nu\in\delta\}\) is the fuzzy \(\mu\)-topology induced over \(\mu\) by \(\delta\). The elements of \(\delta_ \mu\) are called fuzzy \(\mu\)-open sets''. The authors introduce the concepts of \(\mu\)-closed sets, the \(\mu\)- neighbourhood of a fuzzy point, the \(\mu\)-basis of \(\delta_ \mu\), the \(\mu\)-local base at a point, fuzzy \(\mu\)-continuity, \(\mu\)-interior, \(\mu\)-closure, the \(\mu\)-isolated point and they investigate some usual topological properties. The authors finally introduce the concepts of \(\mu\)-prefilter, fuzzy \(\mu\)-ultrafilter, \(\mu\)-convergence and fuzzy compactness and characterize some fuzzy topological concepts via \(\mu\)- convergence.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54B05
zbMATH DE Number: 516660
zbMATH Keywords: fuzzy subspace
zbMATH Keywords: \(\mu\)-prefilter
zbMATH Keywords: \(\mu\)-convergence
zbMATH Keywords: fuzzy compactness
Wikidata QID: Q57820445
author: Marta Macho Stadler
author: María Angeles de Prada Vicente
reviewed by: S. Saha
MaRDI profile type: Publication
cites work: Q5663077
cites work: Fuzzy topological spaces
cites work: Convergence in fuzzy topological spaces
cites work: Q3721382
cites work: Fuzzy filters
full work available at URL: 0165-0114(93)90510-o
OpenAlex ID: W1983527080
description: scientific article; zbMATH DE number 516660