Thread: Base Topology Proof

For topologoical spaces (Τ₁,X₁) and (Τ₂,X₂),
{(G₁ x G₂)| G₁ ∈ Τ₁; G₂ ∈ Τ₂ is a base for the product topology T_{(X1 x X2)}

We know:
B is a base for Τ iff
(1) B⊆Τ and,
(2) For every G∈Τ, if p∈G, then there is B∈B such that p∈B⊆G.