1. The problem statement, all variables and given/known data An example of a function that is open but not closed, and an example of a function that is closed but not open. 2. Relevant equations The function f is open (closed) if f[A] is open (closed) for each open (closed) set A in X. 3. The attempt at a solution This is a topology question and I don't understand it. The only attempt I have made was to guess at a function with < instead of =. If somebody could clarify on the point of what these "functions" look like. Are they the standard, f(x) = x^2 type, or something else?