Hyperspaces of separable Banach spaces with the Wijsman topology

Kubiś, Wiesław; Sakai, Katsuro; Yaguchi, Masato

doi:10.1016/j.topol.2004.07.009

Cited by 11 publications

(4 citation statements)

References 23 publications

(10 reference statements)

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“…A topological semilattice X is called a Lawson semilattice if it has a base of the topology consisting of subsemilattices. Lawson semilattices often appear in the theory of hyperspaces, see [20], [14], [15], [16], [19], [17], [18].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

The strong universality of ANRs with a suitable algebraic structure

Banakh

2021

Preprint

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Let M be an ANR space and X be a homotopy dense subspace in M . Assume that M admits a continuous binary operation * : M × M → M such that for every x, y ∈ M the inclusion x * y ∈ X holds if and only if x, y ∈ X. Assume also that there exist continuous unary operations u, v : M → M such that x = u(x) * v(x) for all x ∈ M . Given a 2 ω -stable Π 0 2 -hereditary weakly Σ 0 2 -additive class of spaces C, we prove that the pair (M, X) is strongly (Π 0 1 ∩ C, C)-universal if and only if for any compact space K ∈ C, subspace C ∈ C of K and nonempty open set U ⊆ M there exists a continuous map f :This characterization is applied to detecting strongly universal Lawson semilattices.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

The strong universality of ANRs with a suitable algebraic structure

Banakh

2021

Preprint

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“…Lemma 1 [11,Theorem 5.1] . Let X be a metrizable Lawson semilattice with Y ⊂ X, a dense subsemilattice.…”

Section: Definitionmentioning

confidence: 99%

A topological position of the set of continuous maps in the set of upper semicontinuous maps

Yang

2009

Sci. China Ser. A-Math.

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Let (X, ρ) be a metric space and ↓USCC(X) and ↓CC(X) be the families of the regions below all upper semi-continuous compact-supported maps and below all continuous compact-supported maps from X to I = [0, 1], respectively. With the Hausdorff-metric, they are topological spaces. In this paper, we prove that, if X is an infinite compact metric space with a dense set of isolated points,Combining this statement with a result in our previous paper,if X is an infinite compact metric space. We also prove that, for a metric space X, (↓USCC(X), ↓CC(X)) ≈ (Σ, c0) if and only if X is non-compact, locally compact, non-discrete and separable.

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“…{y ∈ X : ρ(x, y) < ε} {y ∈ X : inf a∈A ρ(a, y) < ε}. E, F ∈ Cld(X), Hausdorff : f ∈ USC(X) , {x ∈ X : 10,11].…”

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