Theorem

Letandbe open balls in a metric spaceand letthen a ball open inexists such that

Proof

LetandSupposeso there exists

Sincethere exists an open balland sincethere exists an open ball

Takethenandso

Theorem

Letandbe open balls in a metric spaceand letthen a ball open inexists such that

Proof

LetandSupposeso there exists

Sincethere exists an open balland sincethere exists an open ball

Takethenandso