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

作者：Villanueva Hugo^*

来源：Topology and Its Applications, 2016, 197: 28-49.

DOI：10.1016/j.topol.2015.10.006

• Arc-smooth
• Cone
• Continuum
• Dendrite
• Embedding
• Hyperspace
• Whitney levels

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).

• 出版日期2016-1-1