Which of the following is NOT a topology condition?
- Union of open sets is open
- Intersection of any open sets is open
- Empty set is open
- Arbitrary union of closed sets is closed
Explanation
Three axioms define a topology:
The empty set and the whole space must be open.
The union of any collection of open sets must be open.
The intersection of a finite number of open sets must be open.
Why is option B incorrect?
While the intersection of a finite number of open sets is open, the intersection of an infinite number of open sets is not necessarily open.
This is a key distinction in the definition of a topology.
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