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Given a metric continuum X, let C(X) be the hyperspace of subcontinua of X and Cone(X) the topological cone of X. We say that a continuum X is ordered cone-embeddable in C(X) provided that there is an embedding h from Cone(X) into C(X) such that, for each x in X, h(x,0)={x} and h(x,s) is properly contained in h(x,t) whenever s<t. In this paper, we prove that arc-smooth continua X are ordered cone-embeddable...
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