Indecomposable continua

A non-chainable plane continuum with span zero

“…In this paper, we give an example showing that in general span zero does not imply chainable, even among continua in the plane. This example also provides a negative answer to a question of Mohler (Problem 171 of [5], Problem 7 of [10], and Problem 32 of [22]), which asks whether every weakly chainable atriodic tree-like continuum is chainable.…”