▁of ▁an ▁n - tuple ▁provides ▁one ▁natural ▁way ▁in ▁which ▁to ▁build ▁the ▁structure ▁of ▁an ▁object . ▁ ▁Ex amples ▁include ▁- dimensional ▁vector ▁spaces ▁and ▁manif olds , ▁geomet ries ▁and ▁fib re ▁bund les . ▁ ▁Further ▁structure ▁may ▁be ▁assigned ▁to ▁the ▁coordinate ▁space ▁through ▁the ▁coordinates . ▁For ▁example , ▁an ▁- dimensional ▁- vector ▁space ▁may ▁be ▁defined ▁as ▁a ▁coordinate ▁space ▁with ▁the ▁added ▁structure ▁of ▁- linear ity ▁in ▁each ▁of ▁its ▁ ▁coordinates . ▁ ▁It ▁is ▁in ▁general ▁possible ▁to ▁assign ▁a ▁different ▁mapping ▁from ▁a ▁new ▁set ▁of ▁coordinates ▁to ▁the ▁same ▁coordinate ▁space , ▁as , ▁for ▁example ▁with ▁a ▁change ▁of ▁basis ▁for ▁a ▁vector ▁space . ▁ ▁It ▁is ▁not ▁necessary ▁that ▁every ▁n - tuple ▁from ▁the ▁cart esian ▁product ▁of ▁the ▁coordinate ▁sets ▁maps ▁to ▁an ▁element ▁of ▁the ▁space , ▁nor ▁is ▁it ▁necessary ▁that ▁every ▁element ▁have ▁a ▁unique ▁set ▁of ▁coordinates . ▁ ▁For ▁example , ▁a ▁ge ographic ▁coordinate ▁system ▁might ▁assign ▁coordinates ▁of ▁latitude ▁and ▁longitude ▁to ▁locations ▁on ▁the ▁surface ▁of ▁the ▁Earth , ▁but ▁here ▁it ▁will ▁be ▁necessary ▁either ▁to ▁const rain ▁the ▁allowed ▁coordinate ▁pairs ▁or ▁to ▁allow ▁distinct ▁sets ▁of ▁coordinates ▁for ▁the ▁same ▁points . ▁ ▁See ▁also ▁Real ▁coordinate ▁space , ▁R n ▁Complex ▁coordinate ▁space , ▁C n ▁Ex amples ▁of ▁vector ▁spaces ▁ ▁Category : Linear ▁algebra <0x0A> </s> ▁K od um udi ▁block ▁is ▁a ▁re venue ▁block ▁in ▁the ▁E