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UP TGT Mathematics Real Analysis Test Series - Part 3

Cantor's Intersection Theorem requires the nested sequence of non-empty closed sets in a complete metric space to have d...

Type: MCQ • Marks: 1
Cantor's Intersection Theorem requires the nested sequence of non-empty closed sets in a complete metric space to have diameters tending to:
Options
A. Constant c
B. Infinity
C. 1
D. Zero
Explanation
Correct Answer: Option 4 (Zero). 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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