,.hello there,.,i need some hint for this agen,.,
Let S={all (x,y) with x and y rational numbers}
Show that the complement is a polygon connected set. is it an open set??
thnx
I assume that you mean polygonally line connected. Here's a way to think about it, isn't the set equal to $\displaystyle \displaystyle \bigcup_{x\in\mathbb{R}-\mathbb{Q}}\left(\{x\}\times\mathbb{R}\cup\text{x-y axis}\right)\cup\bigcup_{y\notin\mathbb{Q}}\left( \mathbb{R}\times\{y\}\cup\text{x-y axis}\right)$? Draw that out and I think you'll have your answer.