PRINSIPI DUGONIYaT

PRINSIPI DUGONIYaT, prinsipest, ki dar baze qismathoi ma­tematika istifoda meshavad va manii zerin dorad: ba har yak tasdiqoti durusti in qismati matema­tika guftori dugonae muvofiq me­oyad, ki az tasdiqoti avvala dar surati bo mafhumhoi digar — ba istiloh dugona —ivaz kardani mafhumhoi tarkibii vay hosil mesha­vad.

1) Prinsipi dugoniyat dar geometriyai proektivi. In jo Prinsipi dugoniyat dar hamvori muqarrar karda meshavad. Mafhumhoi dugona inhoand: «nuqta» va «khati rost», «nuqta dar khati rost voqe ast» va «khati rost az nuqta meguzarad». Baroi dar yak tasdiqot guftori dugonaero yoftan mumkin ast, ki tavassuti khudi hamin aksiomaho muayyan karda meshavad.

2) Prinsipi dugoniyat dar nazariyai a b st­ran t i i majmuho. Biguzor majmui M doda shuda boshad. Sistemai hamai zermajmuhoi on (A, V, S va gayra)-ro dida mebaroem. Guftori zerin durust ast: agar teorema dar borai zermajmuhoi majmui M, ki tanho bo istilohoti amalhoi sum­ma, burish va purkunanda bayon kar­d meshavad, durust boshad, pas teoremae, ki az hamin teorema dar natijai ivaz namudani amalhoi jam va burish muvofiqan bo amal­hoi burish va jam, majmui kholii A bo tamomi majmui M, majmui M bo majmui holii A hosil meshavad, niz durust meboshad. Dar in mavrid purkunandai summa bo burishi purkunandaho, purkunandai burish bo jami purkunandaho ivaz karda me­shavad.

Ad.: Efimov N. V., Visshaya geo­metriya, 5 izd., M., 1971.