hello, i'm looking for example for a closed group in R^2, but its projection on R is not closed. any ideas?
How about the graph G of the equation . It's complement is an open set in : if you choose a point P not on the curve, it is a distance from the curve, so the ball of radius centered at P is contained in . So G is closed.
But its projection onto the x-axis is the interval , which is an open interval.
Is that what you were looking for?