find the example that $\bigcap\limits _n A_n$ is not connected?
10127
Example of a sequence of closed and connected sets whose intersection is disconnected
33495
A limit problem about $a_{n+1}=a_n+\frac{n}{a_n}$
123742
Proving connectedness of the $n$-sphere
136024
Show that the limit does not exist $\lim_{(x, y) \to (0,0)}\frac{5x^2}{x^2 + y^2}$
104016
Limit point of the set $G= \{1/n: n \in \mathbb N\}$?
57644
Lower bounds for ${{2n} \choose {n}}$
36878
Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
89749
Example of a not recursively enumerable set $A \subseteq \mathbb{N}$
112297
Normal + Connected -> Uncountable
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
129227
An example of neither open nor closed set
139593
$(S_0+\ldots + S_n)_{n\geq 0}$ not a Markov chain
17779
Proving the Limit of a Sequence of without the Dominated Convergence Theorem
55366
Prove that $\bigcap_{k = 1}^\infty C_k$ is also compact and connected.
36485
$H_n(X,A) \not \approx \tilde{H}_n(X/A)$
16255
If $\mathop{\mathrm{Spec}}A$ is not connected then there is a nontrivial idempotent
11834
Prove that $\liminf x_n = -\limsup (-x_n)$