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Given a continuum X and n∈N. Let H(X)∈{2X,C(X),Fn(X)} be a hyperspace of X, where 2X, C(X) and Fn(X) are the hyperspaces of all nonempty closed subsets of X, all subcontinua of X and all nonempty subsets of X with at most n points, respectively, with the Hausdorff metric. For a mapping f:X→Y between continua, let H(f):H(X)→H(Y) be the induced mapping by f, given by H(f)(A)=f(A). On the other hand,...
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