Connected space such that (almost) no subspace is connected
51710
Is there an infinite connected topological space such that every space obtained by removing one point from it is totally disconnected?
55661
Existence of two disjoint closed sets with zero infimal distance
30079
Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?
151719
Connected set in $\mathbb{S}^1$
58296
Is totally disconnected space, Hausdorff?
26919
Intersection of Connected Sets
62911
Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
60746
Simply connected does not imply contractible. Is there a nice counter example in $R^2$?
81471
Finite dimensional spaces
126192
Connected, locally connected, path-connected but not locally path-connected subspace of the plane
147961
Characterizing simply connected spaces
59289
Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
73154
Compact subset in colimit of spaces
156520
Intervals are connected and the only connected sets in $\mathbb{R}$
127419
Subspace of Noetherian space still Noetherian
69206
A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
40208
Locally Constant Functions on Connected Spaces are Constant