Mapping chainable continua onto dendroids. (Q1426495)

A (metric) continuum is hereditarily unicoherent if the intersection of any two of its subcontinua is connected. A dendroid is a hereditarily unicoherent and arcwise connected continuum. It is shown that each chainable continuum can be mapped into a dendroid such that all point-inverses consist of at most three points. This theorem extends a result from the author's paper [Bottlenecks in dendroids] (same journal, submitted). As a consequence it follows that there is a mapping that maps a hereditarily indecomposable continuum (the pseudo-arc) into a hereditarily decomposable continuum (a dendroid) such that all point-ins consist of at most three points. This answers Problem 157 of J. Krasinkiewicz (1979) in \textit{H. Cook}, \textit{W. T. Ingram} and \textit{A. Lelek} [Lect. Notes Pure Appl. Math. 170, 365-398 (1995; Zbl 0828.54001)].