# How do I see that a homeomorphism $\sigma$ is an open function?

How do I see that a homeomorphism is an open function ?

Given a homeomorphism $$\sigma: X \rightarrow Y$$ between topological spaces, how do i then see that $$\sigma(V)$$ is open in $$Y$$ for $$V$$ open in $$X$$ ?

I know that $$\sigma$$ has the following properties: bijection, continuous and continuous inverse $$\sigma^{-1}$$.

I see that $$\sigma^{(-1)}(\sigma(V)) = V$$, but does it imply that $$\sigma(V)$$ is open?

Hint. $\sigma^{-1}$ is continuous, hence preimages of open sets under $\sigma^{-1}$ are open and preimages under $\sigma^{-1}$ are images under $\sigma$.