How can I prove that a continuous injective function is increasing/decreasing?
91852
A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.
143174
property of continuous function
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?
145368
How to show $f:Y\to X^{+}$ is continuous?
150699
Show that if $f'$ is strictly increasing, then $\frac{f(x)}{x}$ is increasing over $(0,\infty)$
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
126842
Fixed point in a continuous function
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
131992
A problem on continuous functions
74502
Proving the bijection of a continuous function $f$ such that $|f(x)-f(y)| \geq \log(1+|x-y|) \forall x,y$ in $\mathbb{R}.$
116732
Proving that a continuous map is surjective
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
112409
If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing
120406
$f$ strictly increasing does not imply $f'>0$
50103
Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
155266
Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
90892
Is a function increasing if the derivative is positive except at one point of an interval?