If $A$ is compact and $B$ is closed, show $d(A,B)$ is achieved
2978
A and B disjoint, A compact, and B closed implies there is positive distance between both sets
29303
Cartesian product of compact sets is compact
63529
How to show that this set is compact in $\ell^2$
146146
Proof that a closed subset of a compact space is a compact space
24912
Show that if $fd'=f'd $ and the pairs $f, d $ and $f',d' $ are coprime, then $f=f' $ and $d=d' $.
8015
Compact set plus a closed set is a closed set
103451
Show that $Y$ is locally compact.
50026
Product of compact and closed in topological group is closed
39293
Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $
74311
Proving that the Intersection of any Collection of Compact Sets is Compact
85076
Is it true that $d(x,Y)=d(x,y_0)$ for some $y_0 \in Y$ when $Y$ is closed?
110744
How to prove that a compact set in a Hausdorff topological space is closed?
76764
Find two closed subsets or real numbers such that $d(A,B)=0$ but $A\cap B=\varnothing$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
128457
Show that $T$ is a compact operator
58948
If $A$ is compact, is then $f(A)$ compact?
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.