Connected sets definition
134073
Definitions of connected space
77621
Continuity of function mapping connected set to connected set
109462
Looking for a counter example for non-connected intersection of descending chain of closed connected sets
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
30079
Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?
108052
Does any connected metrizable space with more than one element have uncountably many open sets, each generating a connected subspace?
89506
Union of disjoint sets : Equivalence relations
23225
Union of connected subsets is connected if intersection is nonempty
1453
Prove that the graph is connected
100437
Classification of connected subsets of the real line (up to homeomorphism)
149980
Are there any countable Hausdorff connected spaces?
72556
Is the closure of path-connected set path connected?
156520
Intervals are connected and the only connected sets in $\mathbb{R}$
44563
Weakly Connected Graphs
133633
A question about path-connected and arcwise-connected spaces
123149
Prove that $E$ is disconnected iff there exists two open disjoint sets $A$,$B$ in $X$
116494
What happens to the connectedness of $\mathbb R^2$ when countable many points are removed?