Abstract

Let C(X) be the hyperspace of all subcontinua of a continuum X topologized by Hausdorff metric. For a non-empty closed subset A of a continuum X, consider the following properties: A is a strong non-cut subset, non-block subset, weak non-block subset, shore subset, not a strong center, and non-cut subset of X. The aim of this paper is to study the conditions under which an ordered arc from a singleton to a proper subcontinuum of a continuum X has one of these properties in C(X).

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