Dimension of fuzzy spaces
type: Item
instance of: scholarly article
title: Dimension of fuzzy spaces
zbMATH Open document ID: 0646.54013
DOI: 10.1016/0165-0114(88)90007-3
published in: Fuzzy Sets and Systems
publication date: 1988-01-01T00:00:00Z
review text: To define a notion of dimension for fuzzy spaces, the author introduces a new boundary operator which uses subsets of \(X\times (0,1]\). (It could also be described in terms of fuzzy points.) Since his methods can be based on any subset of \(X\times (0,1]\) having non-empty, convex vertical sections, he works with a generalization of fuzzy topological spaces. The resulting inductive dimension is monotone, regular spaces contain subspaces of all smaller dimensions, and zero-dimensional spaces are totally disconnected.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54F45
zbMATH DE Number: 4054562
zbMATH Keywords: GF-space
zbMATH Keywords: initial subspace
zbMATH Keywords: final subspace
zbMATH Keywords: boundary operator
zbMATH Keywords: inductive dimension
zbMATH Keywords: zero-dimensional spaces
author: Dušan Adnadjević
MaRDI profile type: Publication
full work available at URL: 0165-0114(88)90007-3
OpenAlex ID: W2002608705
cites work: Q3327311
cites work: Fuzzy topological spaces
cites work: Separation axioms in fuzzy topological spaces
cites work: Q3854303
cites work: Initial and final fuzzy topologies and the fuzzy Tychonoff theorem
cites work: Q4095531
cites work: Fuzzy sets
description: scientific article; zbMATH DE number 4054562