# general topology: do you find the example that \$ bigcap limits _n A_n \$ is not connected?

Give an example of a sequence $$(A_n)$$ of the connected subset of $$mathbb {R} ^ 2$$ such that $$A_ {n + 1} subset A_n$$ for $$n in mathbb {N}$$ but $$bigcap limits_n A_n$$ it is not connected

My attempt: I take $$A_n = (- frac {1} {n} -1, frac {1} {n} +1)$$ but $$bigcap limits_ {n = 1} ^ { infty} (- frac {1} {n} -1, frac {1} {n} +1) = (-1,1).$$ what is connected

I can't really find the example that $$bigcap limits _n A_n$$ it is not connected?