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Reflexive families of closed sets

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Yang Z., Zhao D.

Fundamenta Mathematicae

2006

tom 192

nr 2

111-120

Let S(X) denote the set of all closed subsets of a topological space X, and C(X) the set of all continuous mappings f:X → X. A family 𝓐 ⊆ S(X) is called reflexive if there exists ℱ ⊆ C(X) such that 𝓐 = {A ∈ S(X): f(A) ⊆ A for every f ∈ ℱ}. We investigate conditions ensuring that a family of closed subsets is reflexive.

The Spaces of Closed Convex Sets in Euclidean Spaces with the Fell Topology

100%

Sakai K., Yang Z.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

tom 55

nr 2

139-143

Let $Conv_F(ℝ ⁿ)$ be the space of all non-empty closed convex sets in Euclidean space ℝ ⁿ endowed with the Fell topology. We prove that $Conv_F(ℝ ⁿ) ≈ ℝ ⁿ × Q$ for every n > 1 whereas $Conv_F(ℝ) ≈ ℝ × 𝕀$.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Fundamenta Mathematicae

2 Yang Z.

1 Sakai K.

1 Zhao D.

1 2007

1 2006

Wyniki wyszukiwania

Reflexive families of closed sets

The Spaces of Closed Convex Sets in Euclidean Spaces with the Fell Topology