Generically hereditarily equivalent continua and topological characterization of generic maximal chains of generalized Ważewski dendrites

Abstract The notion of hereditarily equivalent continua is classical in continuum theory with only two known nondegenerate examples (arc, and pseudo-arc). In this paper we introduce generically hereditarily equivalent continua, i.e. continua which are homeomorphic to comeager many subcontinua. We investigate this notion in the realm of Peano continua and we prove that all the generalized Ważewski dendrites are such. Consequently, we study maximal chains consisting of subcontinua of generalized Ważewski dendrites and we prove that there is always a comeager orbit under the natural action of the homeomorphism group. As a part of the proof, we provide a topological characterization of the generic maximal chain.