Topological properties in Whitney blocks

摘要

Let C(X) be the hyperspace of subcontinua of a continuum X. A Whitney block is a set of the form mu(-1) ([s, t]), where mu : C(X) - [0, 1] is a Whitney map and 0 = s t = 1. In this paper, we study the following implication: if X has property P, then each Whitney block in C(X) has property P. We consider the following properties: connectedness im kleinen, being absolute neighborhood retract, local contractibility, and m-mutual aposyndesis. (C) 2018 Elsevier B.V. All rights reserved.