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

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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 $a<b, c<d$

CB

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