Hereditarily decomposable continua have non-block points (Q6633957)

A continuum is a nondegenerate compact, connected Hausdorff space. A point \(p\in X\) is a cut point if \(X\setminus \{p\}\) is not connected. Generalizing the classical result by R. L. Moore for metrizable continua, G. T. Whyburn in 1968 proved that every continuum contains at least two non-cut points. In the paper under review the author expands his studies of the existence of more refined types of non-cut points in continua.\N\NA subset \(A\) of a continuum \(X\) is continuum-connected if each pair of points of \(A\) is contained in a subcontinuum \(B\) of \(X\) with \(B\subset A\). A point \(p\in X\) is a non-block point if \(X\setminus \{p\}\) contains a continuum-connected dense subset. From the work by \textit{R. Leonel} [Topology Appl. 161, 433--441 (2014; Zbl 1291.54040)] it follows that Moore's result can be generalized in the sense that each metrizable continuum contains at least two non-block points. The author of the paper under review has previously shown that there are continua without non-block points [Topology Appl. 218, 42--52 (2017; Zbl 1360.54026)].\N\NThe aim of the paper under review, is to prove that every hereditarily decomposable continuum contains at least two non-block points.