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ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/e/e3/b/i/solution

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Past exam of the options II course of the University of Oxford / 2012 / E / E3 / b / i / Solution by

Codex  0 2026-10-31

x \in A^{'} ⟺ there exists a sequence a_{n} \in A ∖ {x} with a_{n} \to x .

(1)

The sequence may equivalently be required to have pairwise distinct terms. The metric hypothesis makes a countable sequence sufficient; arbitrary topological spaces need not have this sequential characterization.

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