Open connected subset of $ \mathbb R^2 $is path connected
63442
Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
28500
What are the components and path components of $\mathbb{R}^{\omega}$ in the product, uniform, and box topologies?
129943
Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$
77621
Continuity of function mapping connected set to connected set
44704
familly of Radially open sets in $\mathbb{R}^2$
16517
Arcwise connected part of $\mathbb R^2$
19754
$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
2575
Showing that $\mathbb{R}$ is connected
61816
Cut points and connected space
36878
Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
50645
Is the following set (path) connected?
123149
Prove that $E$ is disconnected iff there exists two open disjoint sets $A$,$B$ in $X$
27253
Path connectedness of the set $\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x>0\}$
152442
An annulus in $\mathbb R^2$ is path connected
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
88301
What are all of the connected subsets of $\mathbb{Q}$?
136158
$X$ has Indiscrete topology $\implies$ any subset of $X$ is connected