$\Bbb{R}^2$ not homeomorphic to $\Bbb{R}^2\setminus \{0\}$
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
82458
Homeomorphism between the unit disc and the unit square
142174
Nonexistence of an injective $C^1$ map between $\mathbb R^2$ and $\mathbb R$
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
139176
The real line is not homeomorphic to any non-trivial product space
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
32765
$\mathbb{C}\mathbb{P}^1$ is homeomorphic to $S^2$
1591
What does $\mathbb{R} \setminus S$ mean?
11000
Fundamental group of $\mathbb{R}^2 \setminus (\mathbb{Z} \times \{0\})$
88051
$\mathbb R = X^2$ as a Cartesian product
144072
Are the spaces $\mathbb{H}^n$ and $\overline{\mathbb{R}}^n_+$ homeomorphic?
26197
$B^n/S^{n-1}$ is homeomorphic to $S^n$
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
46365
Single variable complex analysis vs the world of the functions $f:\Bbb R^2 \to \Bbb R^2$.