Topology: is this a convex set?

[Telemachus]

Homework Statement

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.

 

[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?

 

[Telemachus]

Just an opinion question. Thanks Dick.