Closure of a set in arrow topology.

Question

I have to find the closure of a set in topological space $\left(\mathbb{R},\mathcal{T}_{\leftarrow}\right)$. Set is defined as:

$A=\bigcup_{i=1}^{\infty}\left(\frac{1}{2i+1},\frac{1}{2i}\right)$

Can you give me any hints?

Answer 1

Hint: $\frac1{2i}$ is in the closure for all $i\ge1$.