What do the unit balls of this metric look like for radii 1/2, 1 and 3/2 please ?
Radar screen metric is $d(x,y):= \min(1, \|x - y\|_2)$, where the subscript $2$ after the last $\|$ indicates it's over $\mathbb{R}\times\mathbb{R}$.
Thanks
What do the unit balls of this metric look like for radii 1/2, 1 and 3/2 please ?
Radar screen metric is $d(x,y):= \min(1, \|x - y\|_2)$, where the subscript $2$ after the last $\|$ indicates it's over $\mathbb{R}\times\mathbb{R}$.
Thanks
HINT:
The metric $d$ is identical to the usual metric when $\|x-y\|\le 1$; what does that tell you about the $d$-balls of radii $\frac12$ and $1$?
Now let $x\in\Bbb R^2$ be arbitrary. The open $d$-ball of radius $\frac32$ centred at $x$ contains those points $y\in\Bbb R^2$ such that $d(x,y)<\frac32$. Can you find any point $y\in\Bbb R^2$ such that $d(x,y)$ is not less than $\frac32$?