\(L\)-fuzzy topological groups
type: Item
instance of: scholarly article
title: \(L\)-fuzzy topological groups
zbMATH Open document ID: 0760.54005
DOI: 10.1016/0165-0114(92)90183-5
author: Chunhai Yu
author: Jiliang Ma
published in: Fuzzy Sets and Systems
publication date: 1992-09-27T00:00:00Z
review text: The concept of \(L\)-fuzzy topological groups is introduced as follows: Let \(X\) be a group and \(J\) be an \(L\)-fuzzy topology on \(X\). The pair \((X,J)\) is said to be an \(L\)-fuzzy topological group, if and only if the following conditions are satisfied: (a) The mapping \(g: (x,y)\to xy\) of the product \(L\)-fuzzy topological space \((X,J)\times(X,J)\) into \((X,J)\) is a continuous order-homomorphism. (b) The mapping \(h: x\to x^{-1}\) of \((X,J)\) into itself is a continuous order-homomorphism. Some basic properties are discussed. It is proved that, if \(X\) is a group with \(e\) then, under some conditions, there exists an \(L\)-fuzzy topology \(J\) on \(X\) such that \((X,J)\) is an \(L\)-fuzzy topological group.
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 64935
zbMATH Keywords: \(L\)-fuzzy topological group
reviewed by: S. Saha
MaRDI profile type: Publication
full work available at URL: 0165-0114(92)90183-5
OpenAlex ID: W2081241506
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description: scientific article; zbMATH DE number 64935