when are balls separated

Let (X,d) be a metric space, and let Br(x) be the x-centered open ball of radius r. If d(x,y)r+s, then the balls Br(x) and Bs(y) are separated.

To prove this, suppose that Br(x) and Bs(y) are not separated. Then there exists a zX such that either




In either case,

Title when are balls separated
Canonical name WhenAreBallsSeparated
Date of creation 2013-03-22 15:16:40
Last modified on 2013-03-22 15:16:40
Owner matte (1858)
Last modified by matte (1858)
Numerical id 6
Author matte (1858)
Entry type Example
Classification msc 54-00
Classification msc 54D05