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

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

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