Theorem

|The intersection of a closed setwith a compact setis compact.

Proof

Letbe an open cover ofso that

Thenand sinceis closed is an open cover of

is compact so a finite subcoverof A exists.

Henceandis compact.

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Theorem

|The intersection of a closed setwith a compact setis compact.

Proof

Letbe an open cover ofso that

Thenand sinceis closed is an open cover of

is compact so a finite subcoverof A exists.

Henceandis compact.