Projections Open but not closed I often  read that projections are Open but generally not closed. Unfortunately I do not have a counterexample for not closed available. Does anybody of you guys have?

The example which is mentioned by David Mitra shows that the projections are not closed:

The projection $p: \mathbb R^2 \rightarrow \mathbb R$ of the plane $ \mathbb R^2 $ onto the $x$-axis is not closed. Indeed, the set $\color{red}{F}=\{(x,y)\in  \mathbb R^2 : xy=1\}$ is closed in  $\mathbb R^2 $ and yet its image $\color{blue}{p(F)}= \mathbb R \setminus \{0\}$ is not closed in  $\mathbb R$.


