UP TGT Mathematics Real Analysis Test Series - Part 3
For any set A in a metric space, the closure of A, denoted bar(A), is:
Type: MCQ • Marks: 1
For any set A in a metric space, the closure of A, denoted bar(A), is:
Options
A. The largest open set contained in A
B. The smallest closed set containing A
C. The boundary of A
D. The set of interior points
Explanation
Correct Answer: Option 2 (The smallest closed set containing A). 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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