Connectedness properties of the Higson corona of the half line

Abstract

It is proved that the Higson corona of the half line satisfies the following connectedness properties: The Higson corona of the half line is hereditarily unicoherent; under the Continuum Hypothesis, there are 2c composants of the Higson corona of the half line; the principle of Near Coherence Filters is equivalent to the assertion that the Higson corona of the half line has only one composant; no non-degenerate subcontinuum of the Higson corona of the half line is hereditarily indecomposable; and every non-empty open subset of the Higson corona of the half line contains a non-degenerate indecomposable continuum.