Find an example of metric space which is not true the follow equation $\overline {T(x_0,r)}\subset T[x,r]=\{x:d(x,x_0 \leq r)\}$

Question

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

score 0 · Answer 1 · answered Jan 04 '14 at 20:37

0

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.

answered Jan 04 '14 at 20:37

Ulrik

2,557

thanks sir, but if your answer is complete, i.e whether the solution is com – Madrit Zhaku Jan 04 '14 at 20:38
I'm not sure if I understand what you mean. Are you asserting that the solution is incomplete, or that something is unclear? – Ulrik Jan 04 '14 at 20:44

Find an example of metric space which is not true the follow equation $\overline {T(x_0,r)}\subset T[x,r]=\{x:d(x,x_0 \leq r)\}$

1 Answers1