𝛽([0,∞)) does not contain nondegenerate hereditarily indecomposable continua

Abstract

Bellamy has shown that if A = [ 0 , ∞ ) A = \left [ {0,\infty } \right ) , then β A − A \beta A - A is an indecomposable continuum and every nondegenerate subcontinuum of β A − A \beta A - A can be mapped onto every metric continuum. Thus, it follows that every nondegenerate subcontinuum of β A − A \beta A - A contains a nondegenerate indecomposable continuum. We show, however, that no nondegenerate subcontinuum of β A − A \beta A - A is hereditarily indecomposable. Thus, every nondegenerate subcontinuum of β A − A \beta A - A contains a decomposable continuum as well as a nondegenerate indecomposable continuum.