Open and closed maps

Let \(X\) and \(Y\) be topological spaces and \(f\colon X\to Y\) a function. Then \(f\) is an open map if \(f(U)\) is open in \(Y\) for every open \(U\subseteq X\), and \(f\) is a closed map if \(f(C)\) is closed in \(Y\) for every closed \(C\subseteq X\).