Proposition 4.2.3 ([Proposition 1.5, Fol99]).label Let $\curl{X_j}_{1}^{n}$ be topological spaces, $X=\prods{n}{j=1}X_{j}$, then:

1. (1)

   $\tprods{n}{j=1}\cali{B}_{X_j}\suf\cali{B}_{X}$.

2. (2)

   If $\curl{X_j}_{1}^{n}$ are separable, then $\tprods{n}{j=1}\cali{B}_{X_j}=\cali{B}_{X}$.