 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2007/e/2/i/solution

T_{A} = {A \cap U : U \in T}

. For every open

U \subseteq X

i^{- 1} (U) = A \cap U \in T_{A} .

The inverse-image definition of continuity therefore gives the inclusion is continuous from

(A, T_{A})

(X, T)

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