Question

Give an example of a metric space which is not compact

Answer 1

$\text{$\mathbb{R}$ is complete in its standard metric, but not compact. The open cover} \\R=⋯∪(−3,−1)∪(−2,0)∪(−1,1)∪(0,2)∪(1,3)∪⋯ \text{has no finite subcover.}$