Exist strictly increasing $f \colon \omega _1 \mapsto \mathbb{R}$
87356
Are there any known uncountable transfinite increasing sequences of real numbers?
28191
How to show that a set of discontinuous points of an increasing function is at most countable
6270
Poincaré inequality for a subspace of $H^1(\Omega)$
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
61640
Prove c exists for f:[0,1] -> R
138729
What happens when $\lvert\omega\rvert =1$?
63836
Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
129324
Let $f:[0;1]\to\mathbb R$ be continiously differentiable
83185
How to show countability of $\omega^\omega$ or $\epsilon_0$ in ZF?
13732
$||f||_p\to ||f||_\infty$ under general assumptions
96729
Changing the values of an integrable function $f:[a,b] \to \mathbb R$ countably infinitely many points not a dense subset of $[a,b]$
115417
Continuity of $L^1$ functions with respect to translation
12272
Why $a$ is not an essential singularity and how $f$ can be extended
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
101230
Example of an increasing, integrable function $f:[0,1]\to\mathbb{R}$ which is discontinuous at all rationals?
2677
Baire: Show that $f\colon \mathbb{R}\to\mathbb{R}$ is a polynomial in an open bounded set
20284
Continuous injective map is strictly monotonic