The collection is an open covering of .
Can you give us a finite subcover of that cover?
Can anyone help me to understand why set S =(0,2) for each n in the Natural Numbers is not compact in the most basic way possible?
I know so far that S is compact iff every open cover of S contains a finite subcover.
and i also know that a Set (1/n,3) is a open cover of the set (0,2).
thank you.
(0, 2-(2/n)) is not an open cover. is an open cover for (0,2). Same with .
Even though the above is an open cover for (0,2), it has no finite subcover for (0,2). That means, n should go to infinity to cover (0,2).
The above one is a counterexample why (0,2) is not compact, because a subspace of a space X is compact if and only if every open cover of A by open sets in X has a finite subcover