Purely infinite C*-algebras of real rank zero

We show that a separable purely infinite C*-algebra is of real rank zero if and only if its primitive ideal space has a basis consisting of compact-open sets and the natural map K-0(I) -> K-0(I/J) is surjective for all closed two-sided ideals J subset of I in the C*-algebra. It follows in particular that if A is any separable C*-algebra, then A circle times O-2 is of real rank zero if and only if the primitive ideal space of A has a basis of compact-open sets, which again happens if and only if A circle times O-2 has the ideal property, also known as property (IP).