# question about topology in R^2

• March 27th 2013, 05:47 PM
bha
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.