Giving the example of a set A ⊂ X and a point x ∈ X such that dist(x,A)=d(x,y) for :
1) all y ∈ A
2)a single point y ∈ A
3)exactly 3 points y ∈ A
Does anybody who someone to giving the example to over writing instances and draw pictures ?
Thanks a lot
We shall consider subsets of the plane $X=\Bbb R^2$ endowed with the standard metric.
1) $A$ is a one-point set and $x$ is an arbitrary point or $A$ is a circle and $x$ is its center.
2) $A$ is a convex closed set (for instance, a disk or a straight line) and $x$ is an arbitrary point.
3) $A$ is a triangle and $x$ is the center of its incircle.
At the picture the point $x$ is red, the set $A$ is grey, and the subset of points of $A$ which are closest to $x$ is black.
