This example is the book Functional Analysis by Walter Rudin in page 288 Exercise 3.
If $X$ is a compact Hausdorff space, show that there is a natural one-to-one correspondence between closed subset $X$ and closed ideals of $C(X)$.
This example is the book Functional Analysis by Walter Rudin in page 288 Exercise 3.
If $X$ is a compact Hausdorff space, show that there is a natural one-to-one correspondence between closed subset $X$ and closed ideals of $C(X)$.