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# Theorems in Compactness

TOPO-4LKU1X

Which of the following statements is true regarding compact sets in $\mathbb{R}$?

Select ALL that apply.

A

Every compact subset of $\mathbb{R}$ is closed.

B

A closed subset of a compact set in $\mathbb{R}$ is compact.

C

Let $O_{n}$ be a sequence of compact sets in $\mathbb{R}$ such that $O_{n+1} \subset O_{n}$ for all $n$, then $\bigcap \limits_{n=1}^{\infty} O_{n} \neq \emptyset$