Let be a set with metric , , and . If is finite, is said to be a -distance set.
is called a maximal -distance set if and only if for all , there exists such that . That is, if anything is added to , it is no longer a -distance set.
is called a spherical -distance set if and only if is a -distance set and every element of is a fixed distance from some element , so is a subset of the sphere (http://planetmath.org/SphereMetricSpace) centered at with radius .
For example, let with the box metric: with components of , respectively. Let . Then , so , so is a 2-distance set.
Note: please do not confuse this definition of -distance set with , the -distance set of .
|Date of creation||2013-03-22 14:19:17|
|Last modified on||2013-03-22 14:19:17|
|Last modified by||rspuzio (6075)|