UP TGT Mathematics Real Analysis Test Series - Part 3
The diameter of a bounded set A in a metric space (X, d) is defined as:
Type: MCQ • Marks: 1
The diameter of a bounded set A in a metric space (X, d) is defined as:
Options
A. sum {d(x, y) : x, y in A}
B. average of d(x, y)
C. sup {d(x, y) : x, y in A}
D. inf {d(x, y) : x, y in A}
Explanation
Correct Answer: Option 3 (sup {d(x, y) : x, y in A}). A metric space satisfies non-negativity, symmetry, identity of indiscernibles, and the triangle inequality d(x, z) <= d(x, y) + d(y, z).
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