On the hyperspace suspension of a continuum.
The paper consists of eight sections: 1. Introduction, 2. Definitions, 3. General properties, 4. Aposyndesis, 5. Local connectedness, 6. Cones, 7. A universal map theorem, 8. Hereditarily indecomposable continua. For a continuum \(X\), let \(C(X)\) denote the hyperspace of subcontinua of \(X\) and \({\mathcal F}_{1}(X)\) the space of singletons of \(X\), topologized with the Hausdorff metric. The \textit{hyperspace suspension} \(HS(X)\) is the quotient space \(C(X)/{\mathcal F}_{1}(X)\). The authors prove some properties of this hyperspace, for example: (a) \(HS(X)\) is finitely aposyndetic for each continuum \(X\); (b) if \(F\) is a smooth fan, then \(HS(F)\) is homeomorphic to \(C(F)\); (c) the hyperspace suspension of the Hilbert Cube is homeomorphic to the Hilbert Cube.
scientific article; zbMATH DE number 2056821
scientific article