KO‘P O‘LCHOVLI YEVKLID FAZOLARIDA METRIK VA TOPOLOGIK XOSSALAR TAHLILI
Keywords:
Yevklid fazosi, R^n, metrik fazo, topologik fazo, masofa funksiyasi, ochiq to‘plam, yopiq to‘plam, limit, uzluksizlik, kompaktlik, Heine–Borel teoremasi, konvergensiya.Abstract
Ushbu maqolada ko‘p o‘lchovli Yevklid fazolarida metrik va topologik xossalar o‘rganiladi. Natijalarda ochiq va yopiq to‘plamlar, limitlar, uzluksizlik va kompaktlik tushunchalari metrika orqali tavsiflandi hamda ularning ekvivalent shakllari keltirildi. Shuningdek, fazoda Heine–Borel teoremasi va ketma-ketliklar orqali yaqinlashuv mezonlari asoslandi. Muhokama qismida olingan natijalar funksional analiz, differensial tenglamalar va optimallashtirish bilan bog‘liq holda tahlil qilindi. Xulosa sifatida metrik struktura topologik xossalarning asosiy manbai ekanligi ko‘rsatildi.
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