A fuzzy compactum in a space X is an upper semi-continuous map f : A → [ 0 , 1 ] from a nonempty compact subspace A ⊂ X to the unit closed interval [ 0 , 1 ] such that { x ∈ A : f ( x ) > 0 } is dense in A.
Nov 30, 2021
Nov 30, 2021 · In this paper, we investigate the topological structure of the space of fuzzy compacta of a separable metric space X with the Hausdorff metric.
Let X be compact. The space K(X) is homeomorphic to the separable Hilbert space 2 if and only if X is a non-degenerate Peano continuum.
Semantic Scholar extracted view of "On the topological structure of spaces of fuzzy compacta" by Lili Zhang et al.
We prove that the space of fuzzy compacta in a Peano continuum is homeomorphic to the Hilbert space ℓ ... the topological structure of spaces of fuzzy compacta'.
Oct 22, 2024 · We prove that the space of fuzzy compacta in a Peano continuum is homeomorphic to the Hilbert space ℓ2. As a corollary we find that the ...
Semantic Scholar extracted view of "The topological structure of the space of fuzzy compacta" by Wenjuan Liu et al.
Abstract. We study the family of all fuzzy sets of the n-dimensional Euclidean space, which are upper- semicontinuous, fuzzy convex and normal with compact ...
A fuzzy topological space is called a fuzzy Hausdorff space if and only if (iff), for any two distinct fuzzy points p, q of X, there exist disjoint open sets U ...
We study the family of all fuzzy sets of the n-dimensional Euclidean space, which are upper-semicontinuous, fuzzy convex and normal with compact supports ...
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