Abstract
If X is a continuum and μ a Whitney map for C( X), a subcontinuum Y of C( X) is μ-conical pointed if for some λ ∈[0, 1), the cone K(μ −1(λ) ⌢ Y) of μ −1(λ) ⌢ Y is homeomorphic with μ −1[λ, 1] ⌢ Y. This property generalizes the Roger's cone = hyperspace property. If X is a (smooth) dendroid, x ∈ X is a shore point if there is a sequence of subdendroids of X not containing x which converges to X. In this paper we give necessary and sufficient conditions on X, involving shore points, for C p ( X) to be μ-canonical pointed.
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