Hyperspaces of finite sets in universal spaces for absolute Borel classes

• Autorzy: Mine K. , Sakai K. , Yaguchi M.

Identyfikatory

DOI

10.4064/ba53-4-6

• 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 ℓ^f₂ (τ) the linear span of the canonical orthonormal basis of ℓ₂ (τ). It is shown that if E = ℓ^f₂ (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.

Słowa kluczowe

EN

hyperspace of finite subsets; Vietoris topology; Hausdorff metric; universal spaces; absolute Borel classes; Hilbert space; absorbing set

PL

topologia Victorisa; miara Hausdorffa; przestrzeń Hilberta; zbiór pochłaniający

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 4
• Strony: 409--419
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Mine K.

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

autor

Sakai K.

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

autor

Yaguchi M.

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

Bibliografia

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