UP TGT Mathematics Real Analysis Test Series - Part 3
A subset A of a metric space is called PERFECT if:
Type: MCQ • Marks: 1
A subset A of a metric space is called PERFECT if:
Options
A. A' = ∅
B. A is open and dense
C. A is bounded and countable
D. A is closed and A' = A (every point is a limit point)
Explanation
Correct Answer: Option 4 (A is closed and A' = A (every point is a limit point)). Dense sets have closure equal to the space (e.g., Closure(Q) = R). A set is perfect if it is closed and equals its derived set (A = A').
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