Clopen evaluation embedding
= Clopen evaluation embedding
{title2=$e(x)=(\mathbf1_U(x))_{U\in\mathcal B}$}
The <characteristic functions> of a <clopen> <topological basis> give a <topological embedding> of a zero-dimensional $T_0$ <topological space> into a product of discrete two-point <topological spaces>. The <separation> axiom makes those <functions> distinguish points, and their coordinate preimages recover the original <topological basis>.