1. ## question about topology in R^2

hello, i'm looking for example for a closed group in R^2, but its projection on R is not closed. any ideas?

2. ## Re: question about topology in R^2

How about the graph G of the equation $y=\ln{x}$. It's complement $G^C$ is an open set in $\mathbb{R}^2$: if you choose a point P not on the curve, it is a distance $\epsilon$ from the curve, so the ball of radius $\frac{\epsilon}{2}$ centered at P is contained in $G^C$. So G is closed.

But its projection onto the x-axis is the interval $(0,\infty)$, which is an open interval.

Is that what you were looking for?

- Hollywood