Hi guys,

I have to find the closure of $\displaystyle K = \left\{ \frac{1}{n} : n\in\mathbb{N} \right\} $, and $\displaystyle A=(0,1)$ in various topologies.

1. In the standard topology, I think $\displaystyle \overline{K} = K \cup \{0\}$, and $\displaystyle \overline{A} =[0,1]$

2. Now, for the finite complement topology, I'm unsure for both K and A.

3. The upper limit topology, I'm also unsure for both K and A.

4. The topology with basis $\displaystyle \left\{(-\infty, a) : a\in\mathbb{R} \right\}$ I think for both K and A is the set of all positive real numbers.

Thanks alot in advance,

HTale.