Show that $C=\cap_{s\in S}C_s$ is compact, connected and non-empty.
26919
Intersection of Connected Sets
29303
Cartesian product of compact sets is compact
2575
Showing that $\mathbb{R}$ is connected
39746
How to prove that given set is a connected subset of the space of matrices?
63529
How to show that this set is compact in $\ell^2$
84492
Can $X$ have compact connected components?
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
83311
Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
57943
If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ is connected.
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
146364
$X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$
102048
Closure of a compact set in Regular space $ X $
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
144383
The closure of a connected set in a topological space is connected
147213
Prove that finite unions of compact sets are compact