Abstract:

In this paper, we study some properties of the set of isolated points of the compact superkernel of compact spaces. For a T_1-space, we prove that I(\lambda X)\subset {\lambda _c}X; i.e., each isolated point in \lambda X must be a compact maximal linked system. Moreover, for an infinite compact space X with I(X)=\emptyset, we prove that I(\lambda X) =\emptyset; i.e., if X is a pointless space, then its superextension \lambda X is also pointless.