# Thread: Is this open cover example correct?

1. ## Is this open cover example correct?

I need to find an open cover of {x: x>0} with no finite subcover. Is this one?

x $\displaystyle \in$(0,1) and $\displaystyle O_x$=(x/2,1)

2. Originally Posted by tn11631
I need to find an open cover of {x: x>0} with no finite subcover. Is this one?

x $\displaystyle \in$(0,1) and $\displaystyle O_x$=(x/2,1)
Why is it even an open cover?

How about $\displaystyle \left\{(n,n+1):n\in\mathbb{N}\cup\{0\}\right\}\cup \left\{B_1(n):n\in\mathbb{N}\right\}$?

3. Originally Posted by Drexel28
Why is it even an open cover?

How about $\displaystyle \left\{(n,n+1):n\in\mathbb{N}\cup\{0\}\right\}\cup \left\{B_1(n):n\in\mathbb{N}\right\}$?
oh, ok. I get it now. Thank you.

4. Originally Posted by tn11631
I need to find an open cover of {x: x>0} with no finite subcover.
Frankly, a simple answer is best.
It did ask for an open covering: $\displaystyle \left\{ {\left( {\frac{1}{n},\infty } \right):\,n \in \mathbb{Z}^ + } \right\}$.
This makes it very clear the you understand the thrust of the question.