Let X be a subspace of $\mathbb R^2$ consisting of points that at least one is rational. Prove that X is path-connected.
15865
Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
73690
If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
55493
Showing that the path-connected component of the identity matrix in a subgroup of $GL_n(\Bbb R)$ is a normal subgroup
117877
Are homotopy equivalent path-connected spaces homotopy equivalent as pointed spaces?
101712
Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
129943
Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$
102598
Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.
152442
An annulus in $\mathbb R^2$ is path connected
133633
A question about path-connected and arcwise-connected spaces
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
18572
Union of a family of connected pairwise not disjoint subspaces is connected
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.
80524
Path-connected and locally connected space that is not locally path-connected
12104
How to prove this result involving the quotient maps and connectedness?