 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2008/e/1/a/ii/solution

For metric spaces, continuity at

x_{0}

means that for every

ϵ > 0

there is

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 both

ϵ

and

x_{0}

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