I am preparing for an exam and trying to solve this exercise about nowhere dense set. I would be very happy if someone could help me.
Let $(X, \tau )$ be a topological space. A set $S\subset X$ is nowhere dense if it does not contain any internal point. Prove that a closed set $C\subset X$ is nowhere dense if and only if it is the boundary of an open set $U\subset X$.
Thank you very much in advance!