 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2008/e/e1/a/ii/solution

For every

ε > 0

there must be a

δ > 0

such that

dist_{X} (x, x_{0}) < δ ⟹ dist_{Y} (f (x), f (x_{0})) < ε .

The choice of

δ

may depend on

x_{0}

and

ε

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