Why isn't $B = \{x \in l_{\infty} : \| x \|_{\infty} \leq 1 \}$ a compact metric space?
99675
A closed ball in $l^{\infty}$ is not compact
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
110744
How to prove that a compact set in a Hausdorff topological space is closed?
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
133152
(X,d) be a compact metric space. For every open cover, show there exists ε > 0 such that ∀𝑥 ∈ X, B(x,ε) is contained in some member of the cover.
128894
About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
126759
Unbounded continuous function on non-compact metric space
12467
Why does this proof work: Closed unit ball in $C_0$ is not compact
7402
Showing a compact metric space has a countable dense subset
83790
Why doesn't $d(x_n,x_{n+1})\rightarrow 0$ as $n\rightarrow\infty$ imply ${x_n}$ is Cauchy?
120623
Unit sphere in $\mathbb{R}^\infty$ is contractible?
101486
Understanding that $A = \{x\in \ell_2: |x_n| \leq \frac{1}{n}, n = 1,2,...\}$ is compact in $l_2$.
51227
Proving that given metric space is complete: $X := (0,\infty)$ and $d:=|\ln(x)-\ln(y)|$
98609
Does pointwise equicontinuous and uniformly equicontinuous implies compactness?
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
102585
Why is $L^{\infty}$ not separable?
100121
Assume that $(\text{X}, T)$ is compact and Hausdorff. Prove that a comparable but different topological space $(\text{X},T')$ is not.