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- W2085803413 abstract "Let X denote a connected, locally path-connected, σ-compact metric space. F ( X ) is the hyperspace of all nonempty finite subsets of X , topologized by the Hausdorff metric. Let E denote a σ-compact subspace of F ( X ) with the property that, for Eϵ E and Fϵ F (X) with E⋐F, Fϵ E . If X admits a Peano compactification X̄ , then E is a σ Z -set in its closure E ̄ in the hyperspace 2 x̄ , and E ̄ is a topological Hilbert cube. We show that E contains an fd-cap set (and is therefore a boundary set) for E ̄ if and only if the remainder X̄ X is locally non-separating in X̄ . In particular, if X= X ̄ is a Peano continuum, then F ( X ) is a boundary set for 2 x ." @default.
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- W2085803413 date "1986-02-01" @default.
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- W2085803413 title "Hyperspaces of finite subsets as boundary sets" @default.
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- W2085803413 doi "https://doi.org/10.1016/0166-8641(86)90081-7" @default.
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