Zero-dimensional spaces are exactly subspaces of generalized Cantor cubes

A generalized Cantor space is a space homeomorphic to \[ \{0,1\}^{\kappa}, \] where \(\{0,1\}\) is discrete and \(\kappa\) is a cardinal. A space is zero-dimensional if it has a basis of clopen sets.

Outline a proof that a space is zero-dimensional if and only if it is homeomorphic to a subspace of a generalized Cantor space.