Show that $X-C$ is connected
115695
If $X$ is a connected subset of a connected space $M$ then the complement of a component of $M \setminus X$ is connected
123061
$X$ metric separable then $C(X)$ separable
114599
$A \cup B$ and $A \cap B$ connected $\implies A$ and $B$ are connected
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
57943
If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ 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.
158850
Is it true that a boundary of a simply connected and bounded set is connected in $\mathbb{C}$?
101712
Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
62911
Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
100437
Classification of connected subsets of the real line (up to homeomorphism)
42811
Product of path connected spaces is path connected
5132
Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
145718
Proving that A connected graph on $n$ vertices is a tree iff it has $n-1$ edges
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.
63442
Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
88301
What are all of the connected subsets of $\mathbb{Q}$?