Open retractions of indecomposable continua
Tom 148 / 2017
Colloquium Mathematicum 148 (2017), 191-194 MSC: Primary 54F15; Secondary 54C10. DOI: 10.4064/cm6912-7-2016 Opublikowany online: 24 February 2017
We show that for each continuum $X$ there exist an indecomposable continuum $Y$ which contains $X$ and an open retraction $r: Y \to X$ such that each fiber of $r$ is homeomorphic to the Cantor set. Furthermore, $Y$ is homeomorphic to the closure of a countable union of topological copies of $X$ in some continuum. This result is a strengthening of a result proved by Bellamy (1971).