Suppose that I have a continuous function $f: X \rightarrow Y$ such that $f(a) = f(b) $ where $a$ and $b$ are points of $X$. Is it the case that we have that either both $a$ and $b$ are open or neither $a$ nor $b$ are open?
Thanks
Suppose that I have a continuous function $f: X \rightarrow Y$ such that $f(a) = f(b) $ where $a$ and $b$ are points of $X$. Is it the case that we have that either both $a$ and $b$ are open or neither $a$ nor $b$ are open?
Thanks