Given the following set
Let $ x \in B[(0,0),1]$ in $\mathbb{R^2} $
(B stands for the closed ball of centre (0,0) and radius 1)
How do I proof that the set $A = B[(0,0),1] - \{x\}$ is not compact by using Lebesgue-Borel definition, i.e. that it doesn't exist a finite subcover for a cover of A?
For all r > 0, $U_r$ = { a : r < d(x,a) } is open.
Cover the space with { $U_r$ : r > 0 }.
Why not just prove it is not compact since it
is not a closed subset of a Hausdorff space?