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SATH (dar matematika)

SATH (dar matematika), yake az mafhumoti asosii geometriya ast, ki dar faslhoi mukhtalifi on manohoi gunogun dorad: 1) mafhumhoi hamvori, bisiyorruya, inchunin baze sathhoi kajro dar geometriyai maktabi meomuzand. Har yak Sathi kaj bo usuli makhsus, beshtar chun joi geometrni nuqtahoe, ki yagon shartro qone megardonand, tarif doda meshavad. Masalan, Sathi kura gufta majmui nuqtahoero menomand, ki az nuqtai dodashuda dar masofai muayyan voqe gardidaand. Mafhumi «Sath» umuman tarif nadorad, onro metavon tanho sharh dod. Masalan, sarhadi jism yo khud izi khati mutaharrikro Sath menomand.
2) Tarifi aniqi matematikii Sath zimni mafhumoti topologiya doda meshavad. Dar in mavrid mafhumi sathi sodda asosi ast, ki onro chun sathi befosila deformatsiyashavanda (kashish, fishurish, qatshavi) metavon tasavvur kard. Aniqtarash, obrazi inikosi gomeomorfi (inikosi baynan yakqimata va befosila)-i sohai dokhilii kvadrat Sathi soddaro tashkil medihad. Nimsfera niz mansubi Sathi sodda ast. Sferai tom boshad, Sathi sodda namebo- shad. Chunin sathhoro Sathi muntazam menomand. Sathe, ki atrofi har yak nuqtai on (ba qadri kofi khurd) sathi sodda ast, Sathi muntazam me- boshad.
Agar geometriyai -differensiali, odatan Sathhoi muntazamro muoina qunad, geometriyai tahlili Sathro chun majmui nuqtahoe muayyan mekunad, ki koordinatahoyashon yagon navi muayyani muodilaro qone megardonand. Masalan, Akh + Vu Eg y Sh 0 — muodilai hamvori, kh2 + u* + g2 — N2 — muodilai sfera.
Sathe, ki bo chunin usul muayyan karda meshavad, timsoli ayonii Geometri nadoshtanash ham mumkin ast. Chunonchi, muodilai kh2 u2 + g2 + 1 = = 0 sferav mavhumro ifoda mekunad, zero dar fazoi haqiqi nuqtae mavjud nest, ki koordinatahoyash muodilai dodashudaro qone gardonda tavonad. Nigared, niz Nazariyai satho.
N. Kodirov, T. Juraev.

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