cartan-kuranishi deerghata pramey

ack manifold "aim" parr paribhaashit ack baahari vibhedak pranali koo dekhate hue, carton-kuranishi deerghata pramey kahata haye kii "deerghaavadhi" kii ack seemit sankhya key baad pranali yaa tou "antarvirodh mein" haye (cumm seey cumm ack 'badey' abhinn manifold koo sweekaar kartaa haye), yaa asambhav haye.
itihas.
iss pramey kaa naam ellie carton aur masateke kuranishi key naam parr rakhaa gayaa haye.
anuprayog.
iss pramey kaa upayog anant-ayami jhooth siddhant mein kiya jaataa haye.

