Evaluation embedding of a normal Hausdorff space
= Evaluation embedding of a normal Hausdorff space
{title2=$e(x)=(f(x))_{f\in C(X,[0,1])}$}
<Continuous functions> $X\to[0,1]$ on a normal <Hausdorff space> separate points and <closed sets> by <Urysohn's lemma>. The evaluation map into the product of their codomains is <injective> and <continuous>. For each point in an <open set>, a coordinate equal to one there and zero outside the <open set> detects a smaller coordinate <neighborhood>, proving the inverse <topology>.