Abstract
Let C(X) be the hyperspace of subcontinua of a continuum X. A Whitney block in C(X) is a set of the form μ−1([s,t]), where μ:C(X)→[0,1] is a Whitney map and 0≤s<t<1. In this paper we study topological properties P satisfying the implication: if X has property P, then each Whitney block in C(X) has property P. We also consider the converse implication.We study properties related to local connectedness, arcwise connectedness, property of Kelley, contractibility, aposyndesis, unicoherence, etc.
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