If $A$ and $B$ form a separation of $X\setminus Y$, then $Y\cup A$ and $Y\cup B$ are connected
28641
Suppose $Y\subset X$ and $X,Y$ are connected and $A,B$ form separation for $X-Y$ then, prove that $Y\cup A$ and $Y\cup B$ are connected
26919
Intersection of Connected Sets
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
158189
If $\{E_\alpha\}$ is connected, $\bigcap\limits_{\alpha\in A}E \neq \emptyset$, then $\bigcup\limits_{\alpha\in A}E$ is connected
112731
If $Y$ is connected, why is $A\cup Y$ connected in this case?
86505
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
26302
Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
64586
How to prove that $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$
44673
$M$ connected $\iff$ $M$ and $\emptyset$ are the only subsets of $M$ open and closed at the same time
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
12472
Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
153492
Let $p\colon X \to Y$ be a quotient map then if each set $p^{-1}({y})$ is connected, and if $Y$ is connected, then $X$ is connected.
138199
Proof explanation $A\setminus B = A \setminus B \cap A$