I was reading on Wikipedia that
"The maximum modulus principle can be viewed as a special case of the open mapping theorem, which states that a nonconstant holomorphic function maps open sets to open sets. If $|f|$ attains a local maximum at $a$, then the image of a sufficiently small open neighborhood of $a$ cannot be open. Therefore, $f$ is constant".
Could someone expand upon that? I don't follow why the image of a open neighborhood of a would not be open?