Let . Give an example of an open cover of which has no finite subcover.

I was thinking, since it specifies exactly that , then do our open sets (that are in the open covers) have to be open in , or can they be open in ?

For example, if is any rational number in then the set is open in , and the collection of all sets {x} such that x is a rational number in [0,1] is an open cover which has no finite subcover. But is it permissible for my open sets to be open in ? Or do they have to be open in ?