Prove a set is connected and is a connected component
71916
Quasi-components and components coincide for compact Hausdorff spaces
156520
Intervals are connected and the only connected sets in $\mathbb{R}$
47056
Show that the boundary of a set equals the boundary of its complement
23225
Union of connected subsets is connected if intersection is nonempty
50645
Is the following set (path) connected?
66948
Proving question on sets
111032
Proof of Sets involving the Cartesian Product
35115
Questions on how to prove that a set of connectives is NOT functionally complete
17510
Proving a set is an abelian group.
89264
Connectedness in the Quotient Space
10127
Example of a sequence of closed and connected sets whose intersection is disconnected
136158
$X$ has Indiscrete topology $\implies$ any subset of $X$ is connected
116009
Proving that if a set is both open and closed then it is equal to the real numbers
70538
Intersection and union of simply connected domain
151719
Connected set in $\mathbb{S}^1$
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
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.