Let $\Bbb{Z}_2$ be the $2$-adic integers. There's a bijection
$\psi : \Bbb{Z}_2 \to C$, the Cantor set, defined by $\psi (\sum_{i \geq 0} a_i p^i) = \sum_{i \geq 0} \dfrac{2a_i}{3^{i+1}}$. The text then says that, and I quote,
The definition of the product topology shows that this mapping is continuous, and hence is a homeomorphism, since the spaces in question are compact.
How do they get that, with respect to what product topology? Thanks.