Show that for every compact subset $B$ of $X$ disjoint from $A$ $\mathrm{dist}(A,B)>0$.
2978
A and B disjoint, A compact, and B closed implies there is positive distance between both sets
116542
Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$[NBHM_PhD Screening Test-2013, Topology]
147213
Prove that finite unions of compact sets are compact
36315
Is $[0,1]$ a countable disjoint union of closed sets?
143586
Is $[0,1]$ a union of family of disjoint closed intervals?
86309
Whether the set $A$ is a compact subset of $M_3(\Bbb R)$.
80180
Discrete and compact subset must be finite
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
7402
Showing a compact metric space has a countable dense subset
11383
Disjoint compact sets in a Hausdorff space can be separated
22131
Prove if nonempty $K \subset\mathbb{R}$ is compact, then both sup $K$ and inf $K$ exist and are elements of $K$.
83311
Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
153573
Counter Example for the union of any number of compact sets is compact in T2-spaces
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.
26215
Proof Verification: Let $D=\{ \frac{1}{n} \mid n\in\mathbb{N} \} \cup\{0\} \subset \mathbb{E}^1$. Prove that $D$ is compact.
146146
Proof that a closed subset of a compact space is a compact space