Let $f:\mathbb{R} \to \mathbb{R}$ be a cont. function that statisfies $|f(x)-f(y)| \ge \log(1+|x-y|)$ then the function $f$ is bijective.
74502
Proving the bijection of a continuous function $f$ such that $|f(x)-f(y)| \geq \log(1+|x-y|) \forall x,y$ in $\mathbb{R}.$
22210
Points of discontinuity of a bijective function $f:\mathbb{R} \to [0,\infty)$
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
15909
Bijection from $\mathbb R$ to $\mathbb {R^N}$
21269
Bijective continuous function between $(0 ,\infty)$ and $\mathbb{R}$.
93964
Proving that $f$ is a bijection from $N$x$N$ to $N$.
117793
Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.
24107
Bijection $f:\mathcal{P}(A)\to(A\to \{0,1\})$
113975
Let $f:\mathbb{R}\to\mathbb{R}$, $f(kx)=f(x)$. Show that if $f$ is continuous at $0$ then $f$ is a Constant function
16092
How to prove that the composition of two surjective functions is surjective
115636
Show that $f$ is either injective or a constant function.
117716
Condition on function $f:\mathbb{R}\rightarrow \mathbb{R}$ so that $(a,b)\mapsto | f(a) - f(b)|$ generates a metric on $\mathbb{R}$
49953
Proving that a function from $N\times N$ to $N$ is bijective.
141114
Question about a bijection between $\mathbb R$ and $\mathbb R \cup \{\infty\}$
105455
Prove that "injective function $f:X\to Y$ exists" and "surjective function $g:Y\to X$ exists" is logically equivalent.
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$