Chainable continua are not C-determined (Q1807582)

The members of a class \(\Lambda\) of continua are said to be \(C\)-determined provided that if \(X,Y \in \Lambda\) and \(C(X)\) is homeomorphic to \(C(Y)\), then \(X\) is homeomorphic to \(Y\) (the symbol \(C(X)\) denotes the hyperspace of all subcontinua of \(X\) with the Hausdorff metric). In this paper it is shown that the class of chainable continua is not \(C\)-determined. This answers a question by \textit{S. B. Nadler} [Hyperspaces of sets, Monogr. Textb. Pure Appl. Math. 49 (1978; Zbl 0432.54007), Questions 0.62].