 Solution

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

x

means that for every

ε > 0

there is

δ > 0

such that

d_{X} (x, y) < δ

implies

d_{Y} (f (x), f (y)) < ε

for every

y \in X

. Equivalently, the inverse image of each neighborhood of

f (x)

is a neighborhood of

x

 New to topics? Read the docs here!