Question: Let V be a subset of X. a) Prove that V is open in X if and only if there is a collection of open

Let V be a subset of X.
a) Prove that V is open in X if and only if there is a collection of open balls {Ba: a ˆˆ A} such that

V = U Bu- aEA

b) What happens to this result if open is replaced by closed?

V = U Bu- aEA

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