UP TGT Mathematics Real Analysis Test Series - Part 3
The union of an ARBITRARY collection of open sets is:
Type: MCQ • Marks: 1
The union of an ARBITRARY collection of open sets is:
Options
A. Always closed
B. Finite
C. Compact
D. Always open
Explanation
Correct Answer: Option 4 (Always open). Open sets contain neighborhoods around every point; closed sets contain all limit points (complement is open). Int(A) is open, Closure(A) is closed.
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