▁Dom , ▁that ▁is , ▁. ▁View ing ▁zone ▁diag rams ▁as ▁fixed ▁points ▁is ▁useful ▁since ▁in ▁some ▁settings ▁known ▁tools ▁or ▁approaches ▁from ▁fixed ▁point ▁theory ▁can ▁be ▁used ▁for ▁investig ating ▁them ▁and ▁der iving ▁relevant ▁properties ▁( ex istence , ▁ ▁etc .). ▁ ▁Ex istence ▁and ▁uniqu eness ▁Following ▁the ▁pione ering ▁work ▁of ▁As ano ▁et ▁al . ▁( ex istence ▁and ▁uniqu eness ▁of ▁the ▁zone ▁diagram ▁in ▁the ▁e uclidean ▁plane ▁with ▁respect ▁to ▁finit ely ▁many ▁point ▁sites ), ▁several ▁existence ▁or ▁existence ▁and ▁uniqu eness ▁results ▁have ▁been ▁published . ▁As ▁of ▁ 2 0 1 2 , ▁the ▁most ▁general ▁results ▁which ▁have ▁been ▁published ▁are : ▁▁▁ 2 ▁sites ▁( ex istence ): ▁there ▁exists ▁at ▁least ▁one ▁zone ▁diagram ▁for ▁any ▁pair ▁of ▁arbitrary ▁sites ▁in ▁any ▁metric ▁space . ▁In ▁fact , ▁this ▁existence ▁result ▁holds ▁in ▁any ▁m - space ▁ ▁( a ▁general ization ▁of ▁metric ▁space ▁in ▁which , ▁for ▁instance , ▁the ▁distance ▁function ▁may ▁be ▁negative ▁and ▁may ▁not ▁satisfy ▁the ▁triangle ▁inequality ). ▁ ▁More ▁than ▁ 2 ▁sites ▁( ex istence ): ▁there ▁exists ▁a ▁zone ▁diagram ▁of ▁finit ely ▁many ▁compact ▁and ▁dis joint ▁sites ▁contained ▁in ▁the ▁interior ▁of ▁a ▁compact ▁and ▁convex ▁subset ▁of ▁a ▁uniformly ▁convex ▁space . ▁This ▁result ▁actually ▁holds ▁in ▁a ▁more ▁general ▁setting . ▁ ▁More ▁than ▁ 2 ▁sites ▁( ex istence ▁and ▁uniqu eness ): ▁there ▁exists ▁a ▁unique ▁zone ▁diagram ▁with