Sequential completeness of subspaces of products of two cardinals

Let be a cardinal number with the usual order topology. We prove that all subspaces of ² are weakly sequentially complete and, as a corollary, all subspaces of are sequentially complete. Moreover we show that a subspace of (₁ + 1)² need not be sequentially complete, but note that X = A × B is sequentially complete whenever A and B are subspaces of .