compact (idea)

B(0,1)={x \in R²| |x|<1} is not a compact disc, since {B(0,t) | t \in (0,1)} is an open cover with no finite subcover (such a subcover would have a maximal t,t_n, and then B(0,t₀) U B(0,t₁) U ... U B(0,t_n) = B(0,t_n) does not cover B(0,1) since t_n <1).