Let $D = \{(x,y) | x^2 + y^2 < 1\}$, a bounded but not closed, and hence not compact, subset of $\Bbb{E}^2$.
Give an example of an open covering of $D$ with no finite subcovering.
I understand how to do this in $\Bbb{E}^1$ but I can't seem to grasp how to do this beyond knowing that I want to create some infinite union which converges to what is given?
Thank you in advance for the help.
EDIT:
In response to the comment. As an example, if I was doing
$C= \{x \in \Bbb{E}^1 | x \ge 1\}$ then an open covering would be
$\cup_{n=1}^{\infty} (1 , n)$
The above should be the set $[1,\infty)$.
Fingers crossed I haven't completely misunderstood!