Show A neither open nor closed

• Aug 27th 2011, 05:27 PM
rqeeb
Show A neither open nor closed
Show A neither open nor closed in (R^2) , where A={(x,o): -1<x<1}
• Aug 27th 2011, 06:00 PM
Plato
Re: Show A neither open nor closed
Quote:

Originally Posted by rqeeb
Show A neither open nor closed in (R^2) , where A={(x,o): -1<x<1}

Sorry to tell you that question is total nonsense.
If $x=0.5$ the set $(x,0)$ does not exist.

• Aug 27th 2011, 06:13 PM
TheChaz
Re: Show A neither open nor closed
Quote:

Originally Posted by Plato
...

Indeed.
• Aug 27th 2011, 06:16 PM
TheChaz
Re: Show A neither open nor closed
Quote:

Originally Posted by rqeeb
Show A neither open nor closed in (R^2) , where A={(x,o): -1<x<1}

Just use the definitions.
Not open means there exists a point in R^2 such that the ball around this point (for any E > 0) contains a point not in A.
• Aug 27th 2011, 10:08 PM
rqeeb
Re: Show A neither open nor closed
Quote:

Originally Posted by TheChaz
Indeed.

but he Excersize in the book is written by this way:in ${R}^2}$ show that:

$A=\{(x,0):\{-}\1 is neither open nor closed.
• Aug 27th 2011, 10:15 PM
TheChaz
Re: Show A neither open nor closed
Quote:

Originally Posted by rqeeb

but he Excersize in the book is written by this way:in ${R}^2}$ show that:

$A=\{(x,0):\{-}\1 is neither open nor closed.

My first reply was a cheeky way of informing P that HE misread the question.

My second reply is the direction you should go.