Connectedness of $A\cup B$
27581
Topologist's sine curve is connected
10107
Prove $A\cup (A\cap B) = A$
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
74077
A intersection (A union B)
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
39746
How to prove that given set is a connected subset of the space of matrices?
3649
Closed unit interval is connected proof
27899
Can we prove the existence of $A\cup B$ without the union axiom?
27253
Path connectedness of the set $\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x>0\}$
34177
Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
158189
If $\{E_\alpha\}$ is connected, $\bigcap\limits_{\alpha\in A}E \neq \emptyset$, then $\bigcup\limits_{\alpha\in A}E$ is connected
45337
Suppose that $V, W$ are closed in $X$ and that $V\cap W, V\cup W$ are connected. Show that $V$ and $W$ are connected.
18572
Union of a family of connected pairwise not disjoint subspaces is connected
123742
Proving connectedness of the $n$-sphere