Quote by spicychicken
if S_n is the set with empty sets in each index except n where for index n you have [0,1], then {S_n} is an open cover with no finite subcover...i think

Such a sets will always be empty. Try to consider a cover by all sets of the form
[tex]\prod_{n\in \mathbb{N}}{A_i}[/tex]
Where A
_{i}=[0,0.6[ or A
_{i}=]0.5,1]