Show $\mathbb{R}^2 - \mathbb{Q}^2$ is connected.
34177
Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
27188
Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
31266
Proof of "the continuous image of a connected set is connected"
64993
Connectedness of the $S^2$ sphere
114987
How many connected components does $\mathrm{GL}_n(\mathbb R)$ have?
10541
How to prove Mandelbrot set is simply connected?
123742
Proving connectedness of the $n$-sphere
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
138653
Is $\mathbb{R}$ a subspace of $\mathbb{R}^2$?
108394
Proof of that every interval is connected
115583
prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
37589
Connectedness of points with both rational or irrational coordinates in the plane?
22224
Define $S\equiv\{ x\in \mathbb{Q}\mid x^2<2\}$. Show that $\sup S=\sqrt{2} $.
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$