We define a basis property that an inclusion of C^*-algebras O_∞ ⊂ A may have, and give various conditions for the property to hold. Some applications are considered. We also give a characterization of open projections in a corona algebra.

We thank Peter Evanchuck for taking a interest in this work. We thank Eberhard Kirchberg for a copy of his classic unpublished manuscript. We also thank NSERC (Canada) for financial support.