A continuous function $f:\Bbb R\to \Bbb R$ is injective if and only if it is strictly increasing or strictly decreasing
91852
A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.
34260
Injective function from $\mathbb{R}^2$ to $\mathbb{R}$?
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
96273
Is a continuous function $ f\colon(0,\infty)\to R$, such that $f(x)\leq f(nx)$ increasing?
6788
Let $(a,b)$ and $(c,d)$ be intervals in $\Bbb R$, and find an injective and surjective function from $(a,b)$ to $(c,d)$
81488
If a continuous function$f: (X, \mathscr T_X) \to (Y, \mathscr T_Y)$ is injective (Given $Y$ is Hausdorff), show that X is hausdorff
77944
Injective functions with intermediate-value property are continuous. Better proof?
79107
Give an example of a function $f: \mathbb{R} \to \mathbb{R}$ which is continuous only at $0$.
117502
Proving that a certain continuous function is surjective.
140929
Increasing, continuous function implies connectivity and viceversa.
22061
$|f(x)-f(y)|\geq k|x-y|$.Then $f$ is bijective and its inverse is continuous.
45710
Finishing a proof: $f$ is injective if and only if it has a left inverse
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
92089
If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
83461
Continuous iff composition with every linear functional is continuous
44144
If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$