Show that the plane with countably many points removed is path-connected under the Euclidean topology.
116494
What happens to the connectedness of $\mathbb R^2$ when countable many points are removed?
123742
Proving connectedness of the $n$-sphere
135783
Let $T$ and $T^{'}$ be topologies on set $X$ such that $T \leq T^{'}$. If $(X,T^{'})$ is path-connected, is $(X,T)$ path connected?
23414
Topologist's Sine Curve: A rigorous proof of why $\overline{S} = S \cup V$
46469
$n$ Lines in the Plane
114990
Is the complement of countably many disjoint closed disks path connected?
151719
Connected set in $\mathbb{S}^1$
108394
Proof of that every interval is connected
13468
When does open and connected imply path-connected?
147961
Characterizing simply connected spaces
23203
Euclidean distance proof
61816
Cut points and connected space
102484
Connectedness problem and countability of compact subsets of the Sorgenfrey line
137621
The Number of Topologies on a Finite Set
133633
A question about path-connected and arcwise-connected spaces
130361
Basis for a topology with a countable number of sets
36044
Show $\Bbb R ^n$ with a finite set removed is still connected.