open cover

noun

, Mathematics.

1. a cover of a set consisting entirely of open sets.

Example Sentences

The real definition of compactness is that a space is compact if every open cover of the space has a finite subcover.

From Scientific American

So the number line is not compact because we have found an open cover that does not have a finite subcover.

From Scientific American

Now the weird open cover we had no longer covers the whole interval because the points 0 and 1 aren’t any of the intervals.

From Scientific American

It’s harder to show that we couldn’t cook up a different pathological open cover, so you’ll have to take my word for it for now.

From Scientific American

Proving noncompactness only requires producing one counterexample, while proving compactness requires showing that every single open cover of a space, no matter how oddly constructed, has a finite subcover.

From Scientific American