On the Tightness of Product Spaces

This chapter examines the tightness of the topological product of two spaces of tightness ѡ. The chapter proves that if the axiom of constructibility holds, then for each cardinal к there are two Frèchet–Urysson spaces such that the product space has tightness к. Assuming that the continuum is relatively small, it can prove that there are many cardinals under the first measurable cardinal that can be the tightnesses of the product of two spaces with tightness ѡ. The chapter repeatedly refers to the product spaces (Dк)δ and (Nк)δ; noting that for infinite к's they are homeomorphic to (D(2ѡ)к)δ.