ON THE PRODUCT OF METACOMPACT SPACES I. CONNECTIONS WITH HEREDITARY COMPACTNESS.

The concept of a point-additively Noetherian base for a space is defined and is shown to imply hereditary metacompactness. Using a theorem of A. H. Stone on hereditarily compact spaces, it is shown that the property of having a point-additively Noetherian base is finitely productive. In this way a number of famous "counterexamples" are shown to be hereditarily metacom- pact.