# Thread: Show A neither open nor closed

1. ## Show A neither open nor closed

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

2. ## Re: Show A neither open nor closed

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 $\displaystyle x=0.5$ the set $\displaystyle (x,0)$ does not exist.

3. ## Re: Show A neither open nor closed

Originally Posted by Plato
...

Indeed.

4. ## Re: Show A neither open nor closed

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.

5. ## Re: Show A neither open nor closed

Originally Posted by TheChaz
Indeed.

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

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

6. ## Re: Show A neither open nor closed

Originally Posted by rqeeb

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

$\displaystyle A=\{(x,0):\{-}\1<x<1\}$ 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.