 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2008/e/4/b/i/solution

K_{n}

K_{1}

. Any finite intersection equals the member with largest index and is therefore nonempty. The finite intersection property for closed subsets of a compact space implies

n \geq 1 ⋂ K_{n} \neq = \emptyset .

Equivalently, an empty intersection would give an open cover of

K_{1}

by their complements, with a finite subcover contradicting nested nonemptiness.

 New to topics? Read the docs here!