A compact space X is said to be co-Namioka (or to have the Namioka property) if, for every Baire space B and every separately continuous function f : B X → R there exists aG δ dense subset A of B such that f is (jointly) continuous at each point of A X. A collection A of subsets of a topological space X is said to be quasi-closure preserving if all countable subcollections of A are closure preserving.Let X be a compact space. The principal result of this note is slightly more general than the following statement: If there exists a quasi-closure preserving collection A of co-Namioka compact subspaces of X such that X = A, then X is co-Namioka. As an application of this property, we show that the Alexandroff compactification of every locally compact scattered space, which is hereditarily submetacompact, is co-Namioka. In particular, every compact scattered hereditarily submetacompact space has the Namioka property.