$A$ and $B$ are connected spaces and $B$ has limit points of $A$ so $A \cup B$ is also connected
5132
Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
72468
Open and closed balls in $C[a,b]$
36878
Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
146364
$X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
158850
Is it true that a boundary of a simply connected and bounded set is connected in $\mathbb{C}$?
151719
Connected set in $\mathbb{S}^1$
56728
Question about limit points of a Subset of $\mathbb{R}$
86505
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
134073
Definitions of connected space
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?
57943
If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ is connected.
158189
If $\{E_\alpha\}$ is connected, $\bigcap\limits_{\alpha\in A}E \neq \emptyset$, then $\bigcup\limits_{\alpha\in A}E$ is connected
75966
Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
116866
$A\times B$ connected component implies $A,B$ connect components