In Urysohn's Metrization Theorem, at some point we define a function $F : X \rightarrow H$ from the space X into Hilbert space $H$. Whereupon we need to show that $F$ is an embedding. To show this, it apparently suffices to show that $F$ is
- an open mapping.
I don't see how the last two differ?
Continuity is proven with open sets, so is an open mapping?