Pointwise topology on completely distributive lattices
type: Item
instance of: scholarly article
title: Pointwise topology on completely distributive lattices
zbMATH Open document ID: 0667.54001
DOI: 10.1016/0165-0114(89)90179-6
published in: Fuzzy Sets and Systems
publication date: 1989-01-01T00:00:00Z
review text: In the recent years the fuzzy topology has developed considerably. Since all fuzzy sets on a non-empty set form a lattice, the fuzzy topology is a topology on a lattice. Now the author generalizes the theory of fuzzy topology to a theory of pointwise topology on complete, completely distributive lattices. The main topics are following: (1) reconstructing the neighborhood structure, the Q-neighborhoods of fuzzy points are replaced by so-called remote-neighborhoods of molecules. (2) Zadeh's functions between fuzzy topological spaces are replaced by a lattice-wise mapping (so called generalized order-homomorphism). The paper contains a lot of interesting results. Obviously the theory presented here may be furthermore developed.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 06B30
Mathematics Subject Classification ID: 06D10
zbMATH DE Number: 4092311
zbMATH Keywords: molecular lattices
zbMATH Keywords: generalized order-homomorphisms
zbMATH Keywords: minimal families
zbMATH Keywords: maximal families
zbMATH Keywords: molecule
zbMATH Keywords: pointwise topology
zbMATH Keywords: complete, completely distributive lattices
author: Guojun Wang
reviewed by: Yingming Liu
MaRDI profile type: Publication
full work available at URL: 0165-0114(89)90179-6
OpenAlex ID: W1994773895
cites work: Q5331549
cites work: Q3898534
cites work: Topological structures in fuzzy lattices
cites work: \({\mathfrak G}\)-fuzzy topologies on algebraic structures
cites work: Uniformities on fuzzy topological spaces
cites work: Q3219439
cites work: Convergence in fuzzy topological spaces
cites work: Q3685642
cites work: Fuzzy topology. I: Neighborhood structure of a fuzzy point and Moore-Smith convergence
cites work: Q3675158
cites work: Q3733738
cites work: Order-homomorphisms on fuzzes
cites work: A new fuzzy compactness defined by fuzzy nets
cites work: Q3706142
cites work: Q3695311
cites work: Fuzzy sets
cites work: The N-compactness in L-fuzzy topological spaces
description: scientific article; zbMATH DE number 4092311