# Topology: is this a convex set?

1. Sep 10, 2010

### Telemachus

1. The problem statement, all variables and given/known data
Hi there, I have a set similar to this $$\{(x,y)\in{\mathbb{R}^2}:x^2+y^2\neq{k^2},k\in{\mathbb{Z}\}$$ (its the same kind, but with elipses).

And I don't know if it is convex or not. If I make the "line proof", then I should say no. What you say?

Bye there, and thanks.

2. Sep 10, 2010

### Dick

It's the x-y plane with circles (or ellipses) removed, isn't it? I'd agree and say no, not convex. Are you supposed to prove this? Can you? Or is it just an opinion question?

Last edited: Sep 10, 2010
3. Sep 11, 2010

### Telemachus

Just an opinion question. Thanks Dick.