The general fuzzy filter approach to fuzzy topology. I
type: Item
instance of: scholarly article
title: The general fuzzy filter approach to fuzzy topology. I
zbMATH Open document ID: 0873.54008
DOI: 10.1016/0165-0114(95)00058-S
author: Werner Gähler
published in: Fuzzy Sets and Systems
publication date: 1997-10-29T00:00:00Z
review text: The author introduces and investigates a general notion of fuzzy filters (representable by prefilter families), types of fuzzy filters, (sub-)bases of fuzzy filters, fuzzy ultrafilters, principal fuzzy filters and fuzzy filter monad, extending the notions in [\textit{P. Eklund} and the author, in `Applications of category theory to fuzzy subsets', Theory Decis. Libr., Ser. B 14, 110-136 (1992; Zbl 0772.54006); Completions and compactifications by means of monads, in: `Fuzzy Logic: State of Art' (Kluwer, Dordrecht, 1993), 39-56]. The partially ordered monad defined in [the author, in: `Recent developments of general topology and its applications, Internat. conf. in memory of Felix Hausdorff (1868-1942)', Math. Res. 67, 136-149 (1992; Zbl 0803.54013)], turns out to be a submonad of the partially ordered fuzzy filter monad defined by means of the fuzzy filters.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 18C15
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 919470
zbMATH Keywords: prefilter
zbMATH Keywords: fuzzy ultrafilters
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)00058-s
OpenAlex ID: W4232636083
description: scientific article; zbMATH DE number 919470