Expansive homeomorphisms and indecomposable subcontinua (Q1867167)

A compact, connected metric space is called a continuum. It is called \(k\)-cyclic if there exist finite open covers of arbitrary small diameter such that their nerve has at most \(k\) simple closed curves (the nerve of a cover is a graph having its elements as vertices and edges from \(U\) to \(V\) if \(U\cap V \neq\emptyset)\). \textit{H. Kato} [Fundam. Math. 139, 49-57 (1991; Zbl 0823.54028)] posed the question whether a continuum which admits an expansive homeomorphism contains a nondegenerate indecomposable subcontinuum. The paper under review gives a positive answer to this question in case of a \(k\)-cyclic continuum.