Closure of Connected Set is Connected
57122
If $E$ is a connected space, then so is $\overline{E}$.
27661
The closed graph theorem in topology
158189
If $\{E_\alpha\}$ is connected, $\bigcap\limits_{\alpha\in A}E \neq \emptyset$, then $\bigcup\limits_{\alpha\in A}E$ is connected
43584
Separability and normal closure
55486
Topological proof to show a complement set of a set is polygonally connected
70538
Intersection and union of simply connected domain
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.
50645
Is the following set (path) connected?
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
21176
Closure of the set in dictionary order topology.
2575
Showing that $\mathbb{R}$ is connected
13468
When does open and connected imply path-connected?
97373
Is whether a set is closed or not a local property?
127900
Interior of closure of open set in topological space
49374
Closure of a subset in a metric space
44623
Closed set as a countable intersection of open sets
63717
Is the closure of a set equal to the closure of the closure of that set?