 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ib/paper-4/12e/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

For any

ε > 0

, the balls

{B_{ε} (x) : x \in X}

X

. Compactness supplies a finite subcover

X = B_{ε} (x_{1}) \cup \dots \cup B_{ε} (x_{N}) .

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