A note on the class of paracompact spaces whose product with every paracompact space is paracompact

AbstractWe prove that if X is a paracompact space which has a neighborhood assignment x→Hx such that for each y∈X the closure of the set {x∈X:y∈Hx} is compact then the products T×X, for every paracompact space T, and Xω are paracompact. The first result answers a problem of H. Junnila