Hyperspaces which are products
Suppose \(X\) is a continuum. Then \(X\) is a circle or an arc if and only if the hyperspace of subcontinua of \(X\) is a finite dimensional product of two nondegenerate continua. This solves a problem posed by \textit{S. B. Nadler jun.} [ Fundam. Math. 108, 43-66 (1980; Zbl 0456.54023)]. The author also solves another problem of Nadler by giving an example of a non-locally connected continuum whose hyperspace of subcontinua is a cartesian product.
scientific article; zbMATH DE number 1067519
scientific article