Atriodic homogeneous continua
The paper contains a classification of atriodic homogeneous continua. Every such continuum is either a solenoid, or a hereditarily indecomposable continuum, or it has a continuous decomposition to a solenoid with layers homeomorphic to the same hereditarily indecomposable homogeneous continuum. According to Roger's result, every hereditarily indecomposable homogeneous continuum is tree-like. Therefore, in particular, it is obtained that an atriodic homogeneous continuum is 1- dimensional (the answer to a question of \textit{T. Maćkowiak} and \textit{E. D. Tymchatyn} [Diss. Math. 225 (1984; Zbl 0584.54029)]. If every tree-like homogeneous continuum is a pseudo-arc (this is unknown), then, by the above classification theorem, the following continua form a full list of atriodic homogeneous continua: solenoids, the pseudo-arc, the solenoids of pseudo-arcs (analogously in the plane we will have only the following nondegenerate homogeneous continua: the circle, the pseudo-arc, the circle of pseudo-arcs).
scientific article; zbMATH DE number 3883188