Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

The AR-Property of the spaces of closed convex sets

100%

Sakai K., Yaguchi M.

Colloquium Mathematicum

2006

tom 106

nr 1

15-24

Let $Conv_{H}(X)$, $Conv_{AW}(X)$ and $Conv_{W}(X)$ be the spaces of all non-empty closed convex sets in a normed linear space X admitting the Hausdorff metric topology, the Attouch-Wets topology and the Wijsman topology, respectively. We show that every component of $Conv_{H}(X)$ and the space $Conv_{AW}(X)$ are AR. In case X is separable, $Conv_{W}(X)$ is locally path-connected.

Hyperspaces of Finite Sets in Universal Spaces for Absolute Borel Classes

81%

Mine K., Sakai K., Yaguchi M.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

tom 53

nr 4

409-419

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.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Colloquium Mathematicum

2 Sakai K.

2 Yaguchi M.

1 Mine K.

1 2006

1 2005

Wyniki wyszukiwania

The AR-Property of the spaces of closed convex sets

Hyperspaces of Finite Sets in Universal Spaces for Absolute Borel Classes