Nonexistence of a continuous injection from $\mathbb{R}^n$ to $\mathbb{R}$, for all $n \geq 2$.
72644
Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
66272
Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
146188
Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
37206
$\mathbb{R}^n\times\{0\}$ has measure zero in $\mathbb{R}^{n+1}$
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
85175
Continuous Images of $GL_n(\mathbb{R})$
98772
Continuity of a function in $\mathbb{R}$
17525
Why the interior of $\mathbb{Q}$ in $\mathbb{R}$ is empty?
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
24914
Does every continuous map from $\mathbb{Q}$ to $\mathbb{Q}$ extends continuously as a map from $\mathbb{R}$ to $\mathbb{R}$?
93923
No surjective bounded linear map from $\ell^2(\mathbf{N})$ to $\ell^1(\mathbf{N})$
143269
Existence of area-preserving diffeomorphism between two sets in $\mathbb{R}^2$
15095
continuous onto map from $(0,1)\to (0,1]$
22890
Is it coherent to extend $\mathbb{R}$ with a reciprocal of $0$?
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
127114
Differentiability implying continuity
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes