Retractions in hyperspaces.
Given a metric continuum \(X\), let \(2^X\), \(C(X)\) and \(C_2(X)\) denote the hyperspaces of all nonempty closed subsets, subcontinua, and closed subsets with at most two components of \(X\), respectively (with the Hausdorff metric). For a fixed point \(p \in X\) the symbols \(2^X_p\), \(C(p,X)\) and \(C_2(p,X)\) denote the subspaces consisting of these elements of the corresponding hyperspaces that contain the point \(p\). The author studies various mappings between these hyperspaces, especially retractions and (strong) deformation retractions. She characterizes contractibility of \(2^X\) and \(C(X)\) as well as local connectedness of \(X\) in terms of the behaviour of these mappings.
scientific article; zbMATH DE number 2037243