 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2010/e/e1/a/ii/solution

Y

T_{Y} = {Y \cap U : U \in T} .

Y

is open in

X

, every such intersection is open in

X

. Conversely, every ambient open set contained in

Y

equals its intersection with

Y

. Thus the relatively open sets are exactly the ambient open subsets contained in

Y

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