Hyperspaces of Finite Sets in Universal Spaces for Absolute Borel Classes

• Autorzy: Kotaro Mine , Katsuro Sakai , Masato Yaguchi
• Języki publikacji: EN

Abstrakty

EN

By Fin(X) (resp. $Fin^{k}(X)$), we denote the hyperspace of all non-empty finite subsets of X (resp. consisting of at most k points) with the Vietoris topology. Let ℓ₂(τ) be the Hilbert space with weight τ and $ℓ₂^{f}(τ)$ the linear span of the canonical orthonormal basis of ℓ₂(τ). It is shown that if $E = ℓ₂^{f}(τ)$ or E is an absorbing set in ℓ₂(τ) for one of the absolute Borel classes $𝔞_α(τ)$ and $𝔐_α(τ)$ of weight ≤ τ (α > 0) then Fin(E) and each $Fin^{k}(E)$ are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X) is homeomorphic to E and each $Fin^{k}(X)$ is a connected E-manifold.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 54B20: Hyperspaces
• 57N20: Topology of infinite-dimensional manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: 53
• Numer: 4
• Strony: 409-419

Daty

wydano

2005

Twórcy

autor

Kotaro Mine

• Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571 Japan

autor

Katsuro Sakai

• Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571 Japan

autor

Masato Yaguchi

• Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571 Japan

Identyfikatory

DOI

10.4064/ba53-4-6