Is this open cover example correct?

**tn11631** · March 28th 2010, 06:13 PM

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

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

**Drexel28** · March 28th 2010, 06:22 PM

Originally Posted by tn11631

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

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

Why is it even an open cover?

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

**tn11631** · March 28th 2010, 06:27 PM

Originally Posted by Drexel28

Why is it even an open cover?

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

oh, ok. I get it now. Thank you.

**Plato** · March 29th 2010, 07:28 AM

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: $\left\{ {\left( {\frac{1}{n},\infty } \right):\,n \in \mathbb{Z}^ + } \right\}$ .
This makes it very clear the you understand the thrust of the question.

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