“Continuum” denotes
a compact connected Hausdorff space. The principal result is that every
indecomposable continuum can be mapped onto Knaster’s example D of a chainable
indecomposable continuum with one endpoint. This result is then used to conclude
that those indecomposable continua each of whose proper subcontinua is
decomposable, those which are homeomorphic with each of their nondegenerate
subcontinua, and those such that each two points in the same composant can be
joined by a continuum which cannot be mapped onto D, have at least c
composants. It is also shown that generalized arcwise connected continua are
decomposable.
