Proof space is Connected Space
129288
proof that topologist sine curve is not locally connected
136158
$X$ has Indiscrete topology $\implies$ any subset of $X$ is connected
134703
Let $X$ be a connected space, $f:X\to X$ continuous involution, $g:X\to\mathbb{R}$ continuous. Prove that $\exists$ $x\in X$ such that $g(x)=g(f(x))$.
3649
Closed unit interval is connected proof
12104
How to prove this result involving the quotient maps and connectedness?
158189
If $\{E_\alpha\}$ is connected, $\bigcap\limits_{\alpha\in A}E \neq \emptyset$, then $\bigcup\limits_{\alpha\in A}E$ is connected
135256
The fiber of a covering space over a connected space has constant cardinality
116932
Proving a simple graph is a connected graph
83665
Prove a assertion concerning Lebesgue space
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
81220
Space which is connected but not path-connected
101712
Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?
107057
How to show that any separable space is CCC
18039
Let $A$ be a dense subset of $X$ and suppose $A$ is connected in the induced subspace topology, then $X$ is also connected
151719
Connected set in $\mathbb{S}^1$
107076
Prove $S^1$ is not homeomorphic to $S^2$ using connectedness
149980
Are there any countable Hausdorff connected spaces?