Complex projective space CPn is also a compactification of Cn; the Alexandroff one-point compactification of the plane C is (homeomorphic to) the complex projective line CP1, which in turn can be identified with a sphere, the Riemann sphere.
coMpLex prOjEctIVe sPAce cpn iS Also A cOmpActifIcAtIoN of CN; the aLexaNDRoff oNe-poiNT compactiFicatiON oF THe planE C IS (homeomorPhic tO) tHe complEx pRoJectiVe LIne cP1, wHich in turn caN be IdentifIeD wiTh a sphere, the riEmann sPHere.