Set in R^2 which is neither open nor closed.

• November 3rd 2010, 08:53 PM
osodud
Set in R^2 which is neither open nor closed.
Can you mention a set in $R^2$ which is neither open nor closed.

Thanks
• November 3rd 2010, 09:35 PM
Failure
Quote:

Originally Posted by osodud
Can you mention a set in $R^2$ which is neither open nor closed.

Thanks

Let's try a really simple one: $\{(x,0)\in\mathbb{R}^2\mid x\in \;]0,1[\}$
• November 3rd 2010, 11:46 PM
CaptainBlack
Quote:

Originally Posted by osodud
Can you mention a set in $R^2$ which is neither open nor closed.

Thanks

$[a,b[ \times ]c,d]$ , with $a,b,c,d \in \mathbb{R}$ and $a

CB