Lecture 15 (Topology)

In the product topology on X × Y, which statement most accurately describes the collection B = { U × V : U ∈ τ_X, V ∈ τ_Y }?

1. A.B is the full product topology on X × Y
2. B.B is a basis for the product topology, but not every open set is of this form
3. C.B contains only the closed sets of X × Y
4. D.B equals X × Y together with the empty set