Net-convergence in fuzzy neighborhood spaces
type: Item
instance of: scholarly article
title: Net-convergence in fuzzy neighborhood spaces
zbMATH Open document ID: 0930.54004
DOI: 10.1016/S0165-0114(97)00065-1
author: A. F. M. Khodadad Khan
author: T. M. G. Ahsanullah
published in: Fuzzy Sets and Systems
publication date: 2000-01-27T00:00:00Z
review text: The authors introduce a concept of net convergence in Lowen-fuzzy neighborhood spaces. This notion seems to suit fuzzy neighborhood spaces well. For examples, it may be used to characterize Lowen's \(NT_2\) fuzzy neighborhood spaces and cluster points of a set, it is also a good extension of the corresponding notion in topological spaces. The authors prove that a net \((x_d)_{d\in D}\) converges to \(x\) in the product \(X=\prod _{j\in J}X_j\) of fuzzy neighborhood spaces \(\{X_j\}_{j\in J}\) if and only if the net \((p_j(x_d))_{d\in D}\) converges to \(p_j(x)\) in \(X_j\), where \(p_j\) is the projection from \(X\) to \(X_j\) (\(j\in J\)). The notion can also be applied to fuzzy neighborhood groups and fuzzy neighborhood linear spaces to prove certain characterization theorems.
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 1340698
MaRDI profile type: Publication
cites work: On fuzzy neighborhood groups
cites work: On fuzzy neighborhood modules and algebra
cites work: Strictly minimal fuzzy neighborhood division rings
cites work: Invariant probabilistic metrizability of fuzzy neighbourhood groups
cites work: Sequential convergence in fuzzy neighborhood spaces
cites work: Ordered fuzzy topological spaces
cites work: Linear fuzzy neighborhood spaces
cites work: Q3736535
cites work: The categorical topology approach to fuzzy topology and fuzzy convergence
cites work: Fuzzy topological spaces and fuzzy compactness
cites work: Convergence in fuzzy topological spaces
cites work: Fuzzy neighborhood spaces
cites work: Q3685642
cites work: On the Reflectiveness and Coreflectiveness of Subcategories of FTS
cites work: Dual fuzzy neighbourhood spaces. I
cites work: Fuzzy topology. I: Neighborhood structure of a fuzzy point and Moore-Smith convergence
cites work: Fuzzy topology and fuzzy multifunctions
cites work: Q4338293
cites work: Fuzzy nets and their application
cites work: Q4178057
cites work: On the determination of fuzzy topological spaces and fuzzy neighbourhood spaces by their level-topologies
cites work: On separation axioms in fuzzy topological spaces, fuzzy neighborhood spaces, and fuzzy uniform spaces
cites work: Reflectors and coreflectors in the category of fuzzy topological spaces
full work available at URL: s0165-0114(97)00065-1
OpenAlex ID: W1988235172
description: scientific article; zbMATH DE number 1340698