A question that I encountered which looks different than a normal open/closed sets proofs:
Let $(E, d)$ be a metric space, let $f : E\to R$ be continuous and $a$ element of $R$. Show that the set \begin{equation} A = \{x \in\ E : f(x) = a \} \end{equation} is closed.
There is no inequality, instead there is equality, so do we still prove it the same way?
Thank you.
PS. I am a beginner and want to learn these for an exam soon.