 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2009/e/e2/a/i/solution

A

is compact when every open cover of

A

has a finite subcover. This may be stated using sets open in the ambient space or using the subspace topology on

A

; the definitions agree because every subspace-open set is the intersection of

A

with an ambient-open set.

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