$C_0$ is a closed subespace of $l_\infty$?
14840
$c_0$ is a closed subspace of $l^{\infty}$
57868
Prove $\tau$ is cofinite on $X$ iff $(X,\tau)$ is $T_1$-space and any infinite subset of $X$ is dense in $(X, \tau)$
81302
Showing that $a_n \in \ell^{\infty}$
38185
Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
5105
Alternative definition of $\|f\|_{\infty}$ as the smallest of all numbers of the form $\sup\{|g(x)| : x \in X \}$, where $f = g$ almost everywhere
102585
Why is $L^{\infty}$ not separable?
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
146839
Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
125962
The set $A'$ is closed in a $T_1$ space
12467
Why does this proof work: Closed unit ball in $C_0$ is not compact
82355
When is the image of a linear operator (between Banach spaces) closed?
157203
Let $\{f_k\}_{k=1}^\infty\in L^{loc}_1(\mathbb R^n)$, show $\{f_k^2\}_{k=1}^\infty$ does not converge in $\mathscr{D}^\prime(\mathbb R^n)$
73353
Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
156727
A step in the proof of Characterization of $W^{1,\infty}$
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
132491
How to show that $C=C[0,1]$ is a Banach space