Hyperspaces of Keller compacta and their orbit spaces

Antonyan, Sergey A.; Jonard-Pérez, Natalia; Juárez-Ordóñez, Saúl

doi:10.1016/j.jmaa.2013.10.076

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…In this section we will show that the G-space cc(L) is always a G-AE. The technique used to prove this result is based on an argument used in [8] For any Banach space L, denote by L the Banach G-space C(G, L) equipped with the norm (2.1) and the continuous action described in (2.2). Now, if G acts affinely on L, the map Φ : L → L defined by the rule…”

Section: Group Actions By Means Of Affinitiesmentioning

confidence: 99%

“…In this section we will show that the G-space cc(L) is always a G-AE. The technique used to prove this result is based on an argument used in [8] (cf. [1, Theorem C] and [18, Theorem 2],)…”

Section: Group Actions By Means Of Affinitiesmentioning

confidence: 99%

“…Orbit spaces of hyperspaces of convex sets have been studied in the past because of their relation to such classical objects such as the Hilbert cube and the Banach-Mazur compacta BM (n), n ≥ 2 (see e.g. [4], [5], [7] and [8]). In the proof of these results, an important step has been to establish whether or not a certain hyperspace of convex compact sets of a Banach space is an equivariant absolute extensor.…”

Section: Introductionmentioning

confidence: 99%

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Equivariant absolute extensor property on hyperspaces of convex sets

Jonard-Pérez

2014

Topology and its Applications

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Let G be a compact group acting on a Banach space L by means of affine transformations. The action of G on L induces a natural continuous action on cc(L), the hyperspace of all compact convex subsets of L endowed with the Hausdorff metric topology. The main result of this paper states that the G-space cc(L) is a G-AE. Under some extra assumptions, this result can be extended to CB(L), the hyperspace of all closed and bounded convex subsets of L.

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Section: Group Actions By Means Of Affinitiesmentioning

confidence: 99%

“…In this section we will show that the G-space cc(L) is always a G-AE. The technique used to prove this result is based on an argument used in [8] (cf. [1, Theorem C] and [18, Theorem 2],)…”

Section: Group Actions By Means Of Affinitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Equivariant absolute extensor property on hyperspaces of convex sets

Jonard-Pérez

2014

Topology and its Applications

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“…West considered hyperspaces of a group G, equipped with the natural action induced by the group. Since that paper, several results appear in the literature concerning group actions on hyperspaces (see e. g. [1,2,3,5,4,16,17]). Some older results such as [14,18,19] also considered group actions on hyperspaces of convex bodies, but from a convex geometry perspective.…”

Section: Introductionmentioning

confidence: 99%

Some notes on induced functions and group actions on hyperspaces

Donjuán¹,

Jonard-Pérez²,

López-Poo³

2021

Preprint

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Let X be a topological space and CL(X) be the family of all nonempty closed subsets of X.In this paper we discuss the problem of when a continuous map between topological spaces induces a continuous function between their respective hyperspaces. As a main result we characterize the continuity of the induced function in the case of the Fell and Attouch-Wets hyperspaces. Additionally we explore the problem of whether a continuous action of a topological group G on a topological space X induces a continuous action on CL(X). In particular we give sufficient conditions on the topology of G to guarantee that the induced action on CL(X) is continuous, provided that CL(X) is equipped with the Hausdorff or the Attouch-Wets metric topology.

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The Gromov-Hausdorff hyperspace of a Euclidean space, II

Antonyan

2021

Advances in Mathematics

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Hyperspaces of Keller compacta and their orbit spaces

Cited by 5 publications

References 11 publications

Equivariant absolute extensor property on hyperspaces of convex sets

Equivariant absolute extensor property on hyperspaces of convex sets

Some notes on induced functions and group actions on hyperspaces

The Gromov-Hausdorff hyperspace of a Euclidean space, II

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