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Show that U is open set in metric space $(R^2,d_1)$ if and only if U is open set in metric $(R^2,d_{\infty})$

$d_p(x,y)=(\sum^n_1 |x_i-y_i|^p)^\frac{1}{p}$ in $R^n\\$

$d_{\infty}(x,y)=max^n_{i=1} |x_i-y_i|$ in $R^n$

is this metrics are right ..what next

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  • $\begingroup$ Do you have any idea about Equivalent Metrics ?? $\endgroup$ – Nizar Apr 11 '16 at 15:12
  • $\begingroup$ i have little idea $\endgroup$ – user271336 Apr 11 '16 at 15:13
  • $\begingroup$ do you think that this idea can help you in your proof ? Or you are need to follow a specific concept in your proof ? $\endgroup$ – Nizar Apr 11 '16 at 15:15
  • $\begingroup$ i need solution for this one $\endgroup$ – user271336 Apr 11 '16 at 15:16

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