Background: For compact Hausdorff $X$, we can define $C(X)$ the Banach space of continuous functions and $M(X)$ the Banach space of finite signed regular Borel measures on $X$. By the Riesz-Markov theorem $M(X)$ is isometrically isomorphic to $C(X)^*$.
Observation: We can define the following map $\iota:X\to M(X)$ given by $\iota(x)=\delta_x$ where $\delta_x$ is the Dirac delta measure supported at $x$. I can prove that $\iota$ is continuous and homeomorphic onto its image when $M(X)$ is given the weak-* topology. The same should hold for $X$ locally compact Hausdorff and $C_0(X)$ instead of $C(X)$.
Reference Request: What I am looking for is a reference to this fact that I could direct others to (as opposed to having to prove it each time). The more standard the source the better of course. Thanks in advance!