 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2009/e/e3/a/i/solution

U

of a metric space is open if for every

x \in U

there exists

r > 0

with

B_{d} (x, r) \subseteq U

, where

B_{d} (x, r) = {y : d (x, y) < r}

. The radius may depend on the point. The empty set is open vacuously.

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