Let $Q=\{(x,y)\in\mathbb{R}^2|y>x^2\}$. Using the square metric provide a value for $\delta$ so that for any point $(x_0,y_0)\in Q$ the ball $B_{\delta}(x_0,y_0))\subset Q$.
The square metric is given by, \begin{align*} d((x,y),(a,b))=max\{|x-a|,|y-b|\}. \end{align*} I am just so unfamiliar working with the square metric I am having trouble getting a handle on how to compute a specific $\delta$. Any help would be greatly appreciated.