Math, asked by skonline24121999, 6 hours ago

Prove that every open sphere is an open set in a metric space.

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Answered by nshsulthan

Step-by-step explanation:

A set A ⊆ X is open if it contains an open ball about each of its points. ... An open ball in a metric space (X, ϱ) is an open set. Proof. If x ∈ Br(α) then ϱ(x, α) = r − ε where ε > 0.

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Prove that every open sphere is an open set in a metric space.​

Answers

Prove that every open sphere is an open set in a metric space.