Proving this set is compact
101486
Understanding that $A = \{x\in \ell_2: |x_n| \leq \frac{1}{n}, n = 1,2,...\}$ is compact in $l_2$.
22131
Prove if nonempty $K \subset\mathbb{R}$ is compact, then both sup $K$ and inf $K$ exist and are elements of $K$.
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
111032
Proof of Sets involving the Cartesian Product
1409
Proving that the given set has at most $2^{n-1}$ elements
63529
How to show that this set is compact in $\ell^2$
127173
Closed subset of compact set is compact
153934
How to prove that a set R\Z is open
123613
Double Complement of a set proof
110744
How to prove that a compact set in a Hausdorff topological space is closed?
147331
Compactness and Hausdorffness
136583
Infimum is a continuous function, compact set
104308
Proving a set is a Sigma Algebra
79531
Distance between sets with one closed set and one compact set
148994
$K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
83311
Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
8015
Compact set plus a closed set is a closed set