
nirangalude svayamsidhaantham thurakkuka

oru graafinte arikukalkk niram nalkunnathinekkurichulla oru sidhaanthamaanu ooppan colouring axium (churukkatthil oo. sii. eiii), athinte sheershakangal yadhaartha samkhyakalude upavibhagamaananu rund vyathyastha pathippukal avar upayogichum avatharippichum.
prasthavana.
x" ennathu realukalude oru upavibhaagamaanennum "x"-nte oro jody gadakangalkkum karuppum veluppum niramundennum, "x"-leeii poornna graphil velutha jodikalude koottam thurannittundennum karuthuka. ooppan colouring svayamsidhaantham prasthaavikkunnath
durbalamaaya oru pathippaya oo. sii. pii., aadya kesil annamillaatha avasthaye "x" ll othukkamulla thikanja settaayi maattisthaapikkunnu. ekapaksheeyamaayi verthirikkaavunna edangalkku oo. sii. eiii, oo. sii. pii enniva thulyamaayi prasthaavikkam.
mattu sidhaanthangalumaayi bandham.
oru poolish spacinte vishakalana upavibhagangalkkum nirnnayathinte sidhaanthathil ninnum okyaap ZFC yill theliyikkaan kazhiyum. poornnamaaya oo. sii. eiii., zfc-yumayi (ennaal athil ninnu swathanthramaayi) poruthappedunnu, ithu sariyaaya fozhsing axium pinthudarunnu.
parimithikalillaattha ettavum cheria bair spacinu cardinality formula _ 1 undennu ookaa soochippikkunnu. koodaathe, ookaa, bair spacil seekwansukalude settukalkkidayil kurachu "vidavukal" adangiyirikkunnu ennu karuthuka-kooduthal vyakthamaayi paranjaal, saadhyamaaya vidavukal housedorff vidavukalum analogus (κ, ω)-vidavukalum maathramaan, avide κ ennathu ω2 ll kurayaatha prarambha oordinal aanu.

