Let $X$ be a compact Hausdorff space and $\mathcal{A}$ be a closed self-adjoint subalgebra of $C(X)$ which contains teh constants. Then $\mathcal{A}$ is the collection of continuous functions on $X$ which are constant on the sets of $\prod_\mathcal{A}$ where $$ \prod_\mathcal{A}=X/\sim $$ with $x\sim y$ iff $f(x)=f(y)$ for all $f\in\mathcal{A}$.

Could anyone tell me with cited references that who gave the generalized Stone-Weierstrass Theorem above?

Let $X$ be a compact Hausdorff space and $\mathcal{A}$ be a closed self-adjoint subalgebra of $C(X)$ which contains the constants. Then $\mathcal{A}$ is the collection of continuous functions on $X$ which are constant on the sets of $\prod_\mathcal{A}$ where $$ \prod_\mathcal{A}=X/\sim $$ with $x\sim y$ iff $f(x)=f(y)$ for all $f\in\mathcal{A}$.

Could anyone tell me with cited references that who gave the generalized Stone-Weierstrass Theorem above?