On extended fuzzy topologies
type: Item
instance of: scholarly article
title: On extended fuzzy topologies
zbMATH Open document ID: 0942.54004
DOI: 10.1016/S0165-0114(98)00073-6
author: Werner Gähler
author: A. S. Abd-Allah
author: A. Kandil
published in: Fuzzy Sets and Systems
publication date: 2000-02-06T00:00:00Z
review text: This is one of four papers in which the authors develop a theory of extended fuzzy topologies based on fuzzy stacks [J. Fuzzy Math. 6, No. 1, 223-261 (1998; Zbl 0909.54003); ibid., No. 3, 539-574 (1998; Zbl 0913.54007); 575-608 (1998; Zbl 0913.54008)]. Here they present basic results on preimages of fuzzy stacks and fuzzy stack products, on extended fuzzy topologies (characterized by fuzzy neighbourhood stacks and by fuzzy neighbourhoods) and on initial and final extended fuzzy topologies (subspace, product, quotient, sum). The category of extended fuzzy topological spaces is shown to be a complete, cocomplete, topological category and important bireflective and bicoreflective subcategories are studied.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 1400259
zbMATH Keywords: fuzzy filter
zbMATH Keywords: fuzzy neighborhood
zbMATH Keywords: preimage of fuzzy stack
zbMATH Keywords: fuzzy stack product
zbMATH Keywords: fuzzy pretopology
zbMATH Keywords: supra fuzzy topology
zbMATH Keywords: idempotent extended fuzzy topology
zbMATH Keywords: strongly stratified extended fuzzy topology
zbMATH Keywords: initial extended fuzzy topology
zbMATH Keywords: final extended fuzzy topology
zbMATH Keywords: monadic topology
reviewed by: Bernhard Behrens
MaRDI profile type: Publication
Wikidata QID: Q126654530
full work available at URL: s0165-0114(98)00073-6
OpenAlex ID: W2019780392
description: scientific article; zbMATH DE number 1400259