The Cartesian closedness of the category Fuzz and function spaces on topological fuzzes
type: Item
instance of: scholarly article
title: The Cartesian closedness of the category Fuzz and function spaces on topological fuzzes
zbMATH Open document ID: 0826.54003
DOI: 10.1016/0165-0114(94)90176-7
published in: Fuzzy Sets and Systems
publication date: 1995-08-21T00:00:00Z
review text: In some works the category Fuzz consisting of all fuzzes, i.e., all completely distributive lattices with an order reversing involution and all order homomorphisms has been studied and fuzzes topologized. In this paper function spaces are defined on topological fuzzes and the category Fuzz is proved to be Cartesian closed. To study the Cartesian closedness of Fuzz, it is necessary to prove that this category has exponents. To do so, the set of all mappings preserving arbitrary joins is considered and the concept of parallelism of two mappings is introduced. To study function spaces on topological fuzz, the concept of subspaces of a topological fuzz is introduced. Topologies of pointwise convergence and uniform convergence are defined and discussed.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 06D10
Mathematics Subject Classification ID: 18D15
zbMATH DE Number: 788354
zbMATH Keywords: Fuzz
zbMATH Keywords: completely distributive lattices
zbMATH Keywords: order homomorphisms
zbMATH Keywords: Cartesian closedness
author: Zhongqiang Yang
MaRDI profile type: Publication
full work available at URL: 0165-0114(94)90176-7
OpenAlex ID: W2009730774
cites work: Distributivität und subdirekte Zerlegbarkeit vollständiger Verbände
cites work: Products of fuzzy topological spaces
cites work: Uniformities on fuzzy topological spaces
cites work: Q3997287
cites work: Treillis continus et treillis completement distributifs
cites work: Q3733738
cites work: Q4323770
description: scientific article; zbMATH DE number 788354