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Topology

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Compact, Closed and Open Sets of $\mathbb{R}$

TOPO-BKNPSR

Which of the following statements are correct?

A

The set $\{0\} \cup \{\frac{1}{n} |n \in \mathbb{N}\}$ is compact in $\mathbb{R}$.

B

$\mathbb{N}$, the set of all natural numbers, is both closed and open in $\mathbb{R}$.

C

$\{\frac{1}{n} |n \in \mathbb{N}\}$ is compact in $\mathbb{R}$.