Question

prove that a subset of a metric space is open iff it is a union of open balls
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Answer 1

Answer:

here is your answer

Step-by-step explanation:

Bδa(a,d)⊆U. From Superset of Neighborhood in Metric Space is Neighborhood, it follows that U is a neighborhood of x. Since x is arbitrary, it follows that U is a neighborhood of each of its points. Hence by definition, U is open in M.