Show A neither open nor closed

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

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

Please reread and repost a correct question.

Re: Show A neither open nor closed

Quote:

Originally Posted by

**Plato** ...

Please reread and repost ....

Indeed.

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.

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 $\displaystyle {R}^2}$ show that:

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

Re: Show A neither open nor closed

Quote:

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.