I'm taking real analysis and struggling a bit. In class today our professor was saying something about how a function may not be continuous on a non compact set or something, but anyway, he drew the closed interval from 0 to 1 but looped one end back to the middle of the interval. __ | | ---------- Kind of like this, so that an end point and some point in the middle coincide. So my question is, why isn't the looped interval [a,b] compact? Wouldn't it be compact for the same reason [a,b], that is, wouldn't it have the same finite subcover?