PROOFS OF SOME RESULTS REGARDING CLOSED SETS: #proof #results #closed #sets

Here in this page, I gave you proofs of some results regarding closed sets.

Result 1: The sets N,W and Z are closed.

Result 2: The set Q of rational numbers is not closed.

Result 3: If a point p is a limit point of a nonempty set A then each neighborhood contains infinitely many points of A.

Result 4: Union of arbitrary family of closed sets is not closed.

Here we see their proofs.

RESULT 1: The set N of natural numbers is closed.

PROOF :

RESULT 2: The set Q of rational numbers is not closed

PROOF :

RESULT 3: If a point p is a limit point of a nonempty set A then each neighborhood contains infinitely many points of A.

PROOF:

RESULT 4: Union of arbitrary family of closed sets is not closed.

PROOF:

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