Connectedness of subsets of topological space
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.
127900
Interior of closure of open set in topological space
135025
Axiomatization of a Topology using the Boundary
137075
If a topology contains all infinite subsets, then it is the discrete topology
42811
Product of path connected spaces is path connected
88595
Prob. 21, Sec. 17 in Munkres' TOPOLOGY, 2nd ed: Closure and complementation can result in at most 14 different sets
77621
Continuity of function mapping connected set to connected set
120685
Topology induced from Kuratowski Closure properties
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
123742
Proving connectedness of the $n$-sphere
133633
A question about path-connected and arcwise-connected spaces
27661
The closed graph theorem in topology
103717
Topological Property of the Set of Integers
108052
Does any connected metrizable space with more than one element have uncountably many open sets, each generating a connected subspace?
135256
The fiber of a covering space over a connected space has constant cardinality
28766
Intuition behind topological spaces
110744
How to prove that a compact set in a Hausdorff topological space is closed?