On homogeneous hereditarily unicoherent continua

Abstract:

Let $\mathfrak {M}$ denote the class of all hereditarily unicoherent Hausdorff continua in which each indecomposable subcontinuum is irreducible. It is shown that if the continuum $M$ in $\mathfrak {M}$ is decomposable, then the set of weak terminal points of $M$ is a nonempty, proper subset. The following generalization of a theorem of F. Burton Jones is an immediate corollary: if the continuum $M$ in $\mathfrak {M}$ is homogeneous, then $M$ is indecomposable. As an application, it is proved that if $X$ is a homogenous, hereditarily unicoherent Hausdorff continuum which is an image of an ordered compactum, then $X$ is an indecomposable metrizable continuum.