$f:\mathbb{R}\longrightarrow\mathbb{R}$ which is surjective on every open subset of the real line
132223
Function whose image of every open interval is $(-\infty,\infty)$
70264
Prove that the inverse image of an open set is open
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
15418
Why is the space of surjective operators open?
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
93776
Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?
74453
Injective and Surjective Functions
57269
A special bijection between $\mathbb{R}\times \mathbb{R}$ and $\mathbb{R}$
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
27188
Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
117793
Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
100437
Classification of connected subsets of the real line (up to homeomorphism)
154230
In $\mathsf{ZF}$, for each set $A$ exists an ordinal $\alpha$ such that no surjection $A\to \alpha$ exists