Subset of $C[0,1]$ is nowhere dense
132382
Showing a set is nowhere dense in $C([0,1])$
44522
Subsets of the reals when the Continuum Hypothesis is assumed false
67625
$C([0, 1])$ is not complete with respect to the norm $\lVert f\rVert _1 = \int_0^1 \lvert f (x) \rvert \,dx$
74764
Dimension for a closed subspace of $C[0,1]$.
15160
Example of Riemann integrable $f: [0,1] \to \mathbb R $ whose set of discontinuity points is an uncountable and dense set in $[0,1]$
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
53469
C(0, 1) has infinitely many prime ideals not of the form Mp
129205
A question about uncountable, dense sets in R
33309
Subgroup of $\mathbb{R}$ either dense or has a least positive element?
127678
A partition of the unit interval into uncountably many dense uncountable subsets
98391
example of a nonempty subset is closed under scalar multiplication but not a subspace
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
30568
Let $q \in \mathbb C$, $\|q\|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n: n \in \mathbb N\}$ is dense in $S^1$
122463
How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?
43254
If $A\subseteq\mathbb N$ and $\sum\limits_{a\in A}\frac1a$ converges then $A$ has natural density $0$
90590
Prove that the following set is dense
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)