Show that, in $C[0,1]$, the functions with $f(\Bbb Q) \subseteq \Bbb Q$ are dense.
95294
Dense subset of $C[0,1]$ which preserves rationals
28391
Prove the compactness of a set B
90590
Prove that the following set is dense
22865
Sine function dense in $[-1,1]$
122463
How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?
3772
About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
83311
Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
4381
Proof that the set of irrational numbers is dense in reals
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
25795
Density of $\mathbb{Q}^n$ in $\mathbb{R}^n$
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
142901
"The closure of the unit ball of $C^1[0, 1]$ in $C[0, 1]$" and its compactness
29403
Finding functions $f: \Bbb R_*^+ \to \Bbb R_*^+$ with certain properties
128766
Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
53173
Infinitely differentiable functions with compact support are dense in $L^p$
33642
Finite dimensional subspace of $C([0,1])$