The Paranormality of Products and Their Subsets

Abstract

A topological space is called paranormal if any countable discrete system of closed sets {Dn:n = 1, 2, 3,...} can be expanded to a locally finite system of open sets {Un:n = 1, 2, 3,...}, i.e., Dn is contained in Un for all n, and Dm ∩ Un≠ O if and only if Dm = Dn. It is proved that if X is a countably compact space whose cube is hereditarily paranormal, then X is metrizable.