 Solution

ID: past-exam-of-the-metric-spaces-and-complex-analysis-course-of-the-university-of-oxford/2017/1/a/ii/solution

The sequence converges to

x \in X

\forall ε > 0 \exists N \forall n \geq N : d (x_{n}, x) < ε .

Equivalently

d (x_{n}, x) \to 0

. The limit must belong to the specified metric space, not just to a larger space containing it.

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