1. The problem statement, all variables and given/known data Show that S = [0,1) is not compact by giving an closed cover of S that has no finite subcover. 2. Relevant equations 3. The attempt at a solution I know that S is not compact because it is [STRIKE]an open[/STRIKE] not a closed set even though it is bounded. But I am completely lost on the open cover part. I understand an open cover is a union of open sets where S is a subset of the union... But I appear to missing something very fundamental. If I picked (-1, 2) for the cover that is an open set and S is a subset of it's "trivial" union. Why doesn't that work? <edit> OK, I understand it needs to work for every cover, that's why, but is (-1,2) a cover? <end edit> If instead I had [0,1], that is closed and bounded so it is compact. What sort of sets would go into a cover for it? Does anyone know some extremely elementary references for this?