Proof that if $R_{1};R_{2}=R_{2};R_{1}$ is a relation on a set $S$, then $R_{1}$ and $R_{2}$ are bijective maps
97801
If $R_{1}$ and $R_{2}$ are relations on a set S with $R_{1};R_{2}=R_{2};R_{1}$. Then $R_{1}$ and $R_{2}$ are bijective maps
93776
Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?
1707
How does one prove that addition on $\mathbb{R}$ is associative?
15909
Bijection from $\mathbb R$ to $\mathbb {R^N}$
31391
bijection between $\mathbb{N}$ and $\mathbb{N}\times\mathbb{N}$
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
138436
How to prove reflexivity, symmetry and transitivity for the following relation?
146356
To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
85713
Showing Parallelism is an equivalence relation in $\Bbb R ^2$
38378
$M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$
36878
Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
112231
Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set
71977
Give an example of a relation R on $A^2$ which is reflexive, symmetric, and not transitive
95086
Homeomorphism is bijective
12825
Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$