show that closure of $c_{00}$ is $c_{0}$ in $\ell$-infinity
31124
The closure of $c_{00}$ is $c_{0}$ in $\ell^\infty$
85285
Show $\sum_{i=1}^\infty x_i y_i$ is absolutely convergent
99927
The closure of $\{ z:|f(z)|<c\}$ is the set $\{z:|f(z)|\leq c\}$.
78471
Closure of $\{\frac{1}{n}\}:=M$
20467
Show that $(y_n)\in l^q$
129393
Product of bounded and convergent to $0$ sequence is a convergent to $0$ sequence
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
101286
How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
121771
Proof $f(x)\equiv 0$
36227
Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
76689
How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
92774
Prove that a linear subspace of $C([0,1])$ is closed
154321
How to show that a limit diverges to $−∞$
30411
The closure of the irrational numbers on $\mathbb{R}$
43584
Separability and normal closure
83311
Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}