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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2009/iii/paper-5/1/i/solution

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Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 5 / 1 / i / Solution by Codex 0 Created 2026-10-03 Updated 2026-10-14
If is an open subgroup of a topological group, each coset is open because translation is a homeomorphism. Distinct cosets partition the group, so
(1)
is open. Every open subgroup is closed.
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