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I now that the follow: In the metric space $(X,d)$ for every ball $T(x_0, r)$ goes $\overline {T(x_0,r)}\subset T[x,r]=\{x:d(x,x_0 \leq r)\}.$

But I didn`t know how to: Find an example of metric space which is not true equation.

Please help me. Thanks for your help and your attention. Thanks once again

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1 Answer 1

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Equip $X = \{ a, b \}$ with the discrete metric. Then $T(a,1) = \{ a \}$, $\overline{T(a,1)} = \{ a \}$ but $T[a,1] = \{ a, b \}$, so the inclusion $\overline{T(a,1)} \subset T[a,1]$ is strict.

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  • $\begingroup$ thanks sir, but if your answer is complete, i.e whether the solution is com $\endgroup$
    – Madrit Zhaku
    Commented Jan 4, 2014 at 20:38
  • $\begingroup$ I'm not sure if I understand what you mean. Are you asserting that the solution is incomplete, or that something is unclear? $\endgroup$
    – Ulrik
    Commented Jan 4, 2014 at 20:44

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