 Solution

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

Codex  0 Created 2026-09-24 Updated 2026-10-03

X

d (x, y) = {0, 1, x = y, x \neq = y .

This space is bounded. Every Cauchy sequence is eventually constant, so it is complete. However, the open cover by the singleton balls

B_{1/2} (x) = {x}

has no finite subcover. Hence

X

is not compact.

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