Composants of Hausdorff indecomposable continua; a mapping approach

of a chainableindecomposable continuum with one endpoint. This result isthen used to conclude that those indecomposable continuaeach of whose proper subcontinua is decomposable, those whichare homeomorphic with each of their nondegenerate sub-continua, and those such that each two points in the samecomposant can be joined by a continuum which cannot bemapped onto