On the tychonoff functor and w-compactness

The main purpose of this paper is to settle the following problem concerning a product formula for the Tychonoff functor τ, by introducing the notion of w-compact spaces: Characterize a topological space X such that τ(X×Y)=τ(X)×τ(Y) for any topological space Y. We also study the properties of w-compact spaces, and it is proved that, for any family {X_α} of w-compact spaces, the product ΠX_α is also w-compact and τ(ΠX_α)=Πτ(X_α).