Concerning \(k\)-mutual aposyndesis in symmetric products (Q1935837)

A \textit{continuum} is a nonempty compact connected metric space. A continuum \(X\) is \textit{\(k\)-mutually aposyndetic} if for each subset \(A\) of \(X\) with \(k \geq 2\) distinct points there exists \(k\) disjoint subcontinua of \(X\) where each of these subcontinua containing one point of \(A\) in its interior. For a continuum \(X\), let \(F_n(X)\) denote the hyperspace of all nonempty subsets of \(X\) with at most \(n\) points. In the paper under review the authors prove that if \(X\) is a continuum and \(n \geq 3\), then \(F_n(X)\) is \(k\)-mutually aposyndetic for each positive integer \(k\).