I have this topology on $\mathbb{R}^2$:
$$ \sigma=\{\mathbb{R}^2,\emptyset, (B_r)_{r>0}\}$$ where $$B_r=\{(x,y)\in\mathbb{R}^2; (x-3)^2+y^2<r^2\}.$$
The question is to study the nature of the sequence $u_n=(2,\frac1n)$ and to find the adherent value of $v_n=(\frac1n,1)$.
Concerning $u_n$, I found that it is convergent to every $(x,y)$ such that $$(x-3)^2+y^2\geq1 $$.
We say that $l$ is an adherent value for $v_n$ iff $\forall V\in \mathcal{V}_l, \rm card\{n\in\mathbb{N}, v_n\in V\}=+\infty$.
I found that $(x,y)$ is an adherent value of $(v_n)$ iff $(x-3)^2+y^2\geq 10$.
Is it correct or are there other limits or adherent values?
Thank you.