The only endomorphism of $\mathbb{R}$ is identity
30817
Is an automorphism of the field of real numbers the identity map?
95086
Homeomorphism is bijective
12825
Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$
119702
Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
143800
continuous map on $\mathbb{R}$ which is the identity on $\mathbb{Q}$ is the identity map, hence Aut$(\mathbb{R}/\mathbb{Q})= 1.$
52088
Isomorphism of an endomorphism ring, how can $R\cong R^2$?
57269
A special bijection between $\mathbb{R}\times \mathbb{R}$ and $\mathbb{R}$
145077
A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
66866
Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
38378
$M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$
158892
Surjective endomorphism of abelian group is isomorphism
141114
Question about a bijection between $\mathbb R$ and $\mathbb R \cup \{\infty\}$
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
112807
Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
12474
Does an injective endomorphism of a finitely-generated free R-module have nonzero determinant?