Embedding cones over arc-smooth continua into their hyperspace of subcontinua

摘要

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 in C(X). (C) 2015 Elsevier B.V. All rights reserved.