Hints to show that $A_{n}$ is nowhere dense in $C([0,1])$
102250
Subset of $C[0,1]$ is nowhere dense
62977
Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
128766
Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
66897
Cesaro summable implies that $c_{n}/n$ goes to $0$
88523
Show that $A=\{ \frac{m}{2^n}:m\in \mathbb {Z},n\in \mathbb {N} \} $ is dense in $\mathbb {R}$
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
83116
Uncountability of basis of $\mathbb R^{\mathbb N}$
122463
How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?
70298
Are quotients of chain groups $C_n(X)/C_n(A)$ still free?
36485
$H_n(X,A) \not \approx \tilde{H}_n(X/A)$
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
17461
Show that a set is dense in $[-1,1]$
71173
Show that $\mathbb{A}^n$ on the Zariski Topology is not Hausdorff, but it is $T_1$
50019
Prove $0$ is a partial limit of $a_n$
73336
If $A$ is a nowhere dense subset of a topological space $X$, then $X\setminus A$ is dense in $X$.
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$