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  3. 121 given the following definition 121 balls let x d...

Question: 121 given the following definition 121 balls let x d...

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1.2.1 Given the following Definition 1.2.1 (Balls). Let (X, d) be a metric space, let ro be a point in X, and let r >0. We define the bal Bx.d) (ro,r) in X, centered at ro, and with radius r, in the metric d, to be the set When it is clear what the metric space (X,d) is, we shall abbreviate Bixay(ro.r) as just B(ro.r). Verify the following example Example 1.2.8. When we give a set X the discrete metric ddise, and E is any subset of X, then every element of E is an interior point of E every point not contained in E is an exterior point of E, and there are no boundary points; see Exercise 1.2.1

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