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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?

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

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