hyperbolic metric space
A hyperbolic metric space is a metric space that is hyperbolic for some .
Although a metric space is hyperbolic if it is hyperbolic for some , one usually tries to find the smallest value of for which a hyperbolic metric space is hyperbolic.
A example of a hyperbolic metric space is the real line under the usual metric. Given any three points , we always have that . Thus, for any , we can take . Therefore, the real line is 0 hyperbolic. reasoning can be used to show that every real tree is 0 hyperbolic.
|Title||hyperbolic metric space|
|Date of creation||2013-03-22 17:11:29|
|Last modified on||2013-03-22 17:11:29|
|Last modified by||Wkbj79 (1863)|