Show that there is no increasing function $f: \aleph_1 \to \mathbb{R}$
70196
Is there any well-ordered uncountable set of real numbers under the original ordering?
61500
If f is continous and exist real numbers show that $f(x)=0$
99431
Increasing functions are Baire one
148512
No analytic function $f$ has modulus $|f(z)|=1/\cosh(\Re z)$
87027
There is no continuous injective function $f:\mathbb{R}^n\longrightarrow\mathbb{R}^m$
234
No continuous function switches $\mathbb{Q}$ and the irrationals
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
78319
Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0
127921
Does there exist a function such that $\lim_{x \to a} f(x) = L$ for all $a \in \mathbb R$ but $f(x)$ is never $L$?
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
110395
Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
135999
One sided limit of an increasing function defined on an open interval
45432
Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
30036
Function in $H^1$, but not continuous
28764
How do we know an $ \aleph_1 $ exists at all?
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
145573
How to show that $f$ is a zero function?