Hereditarily unicoherent
We say that a continuum $X$ is hereditarily unicoherent if every subcontinuum of $X$ is unicoherent.
Properties
Tree-like implies hereditarily unicoherent
We say that a continuum $X$ is hereditarily unicoherent if every subcontinuum of $X$ is unicoherent.
Tree-like implies hereditarily unicoherent