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- W2010067900 abstract "We write 2 x for the hyperspace of all non-empty compact sets in a complete metric linear space X topologized by the Hausdorff metric. Using the notation F ( X ) = { A ϵ 2 X : A is finite}, l f 2 = { x } = ( x i ) ϵ l 2 : x i = 0 for almost all i }, and l σ 2 = { x = ( x i ) ϵ l 2 :σ ∞ i =1 ( ix i ) 2 < ∞}, we have the following theorem: A family G ⊂ F ( X ) is homeomorphic to l f 2 if G is σ-fd-compact, the closure G of G in 2 x is not locally compact and if whenever A, B ∈ G , λ ∈ [0, 1] and C ⊂ λ A + (1 - λ) B with card C ⩽ max{card A , card B } then C ϵ G . Moreover, for any G δ -AR-set G G of G with G G ⊃ G we have ( G G , G )≅( l 2 , l ƒ 2 ). Similar conditions for hyperspaces to be homeomorphic to l σ 2 are also established." @default.
- W2010067900 created "2016-06-24" @default.
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- W2010067900 date "1986-03-01" @default.
- W2010067900 modified "2023-10-17" @default.
- W2010067900 title "Hyperspaces of compact sets in metric linear spaces" @default.
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- W2010067900 doi "https://doi.org/10.1016/0166-8641(86)90001-5" @default.
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