PROOFS OF FEW RESULTS ON OPEN SETS #proof #few #results #open #sets

PROOFS OF FEW RESULTS 1:

Here we are going to see the proofs of some results what we know.

They are

1. Intersection of an infinite collection of open sets is not open.

2. The set N of natural numbers is not open.

3. Every neighborhood is an open set.

4. Union of any collection of open sets is open.

Now come to proofs :

1. INTERSECTION OF AN INFINITE COLLECTION OF OPEN SETS IS NOT OPEN :

PROOF :

2. THE SET N OF NATURAL NUMBERS IS NOT OPEN:

PROOF :

3. EVERY NEIGHBORHOOD IS AN OPEN SET :

PROOF :

4. UNION OF ANY COLLECTION OF OPEN SETS IS OPEN :

PROOF :

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