UP TGT Mathematics Real Analysis Test Series - Part 3
A set F in a metric space is CLOSED if and only if its complement F^c is:
Type: MCQ • Marks: 1
A set F in a metric space is CLOSED if and only if its complement F^c is:
Options
A. Closed
B. Bounded
C. Open
D. Compact
Explanation
Correct Answer: Option 3 (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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