1
$\begingroup$

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

  • 0
    Hopefully $a$ is a point of $X$ and $b$ is a point of $y$...2012-12-06
  • 0
    @Arthur: That would make the question nonsense, so let's not hope that.2012-12-06
  • 0
    Sorry, I misread the question.2012-12-06
  • 1
    Note that you don't say "$a$ is open", but rather "(the set) $\{a\}$ is open".2012-12-06

1 Answers 1