المجموعة المحدبة وفق المستويات الإحداثية في R3
Abstract
يقال عن مجموعة في الفضاء الإقليدي ثلاثي البعد إنها محدبة وفق المستويات الإحداثية إذا كان تقاطع أيِّ مستوٍ موازٍ لأيٍّ من المستويات الإحداثية مع المجموعة عبارة عن مجموعة محدبة. في هذا البحث قدمنا نمطاً جديداً في التحدب وهو المجموعات المحدبة وفق المستويات الإحداثية, وحصلنا على مجموعة من النتائج والمبرهنات أهمها إثبات أن كل مجموعة محدبة وفق المستويات الإحداثيةهي مجموعة محدبة, وعرضنا العديد من الأمثلة التي توضح العلاقة بين المجموعات النجمية والمتراصة وأحادية الترابط والمحدبة إحداثياً والمحدبة وفق المستويات الإحداثية. Let A be a set in R3. A is called a Convex set in accordance with the coordinate planes ,if and only if ,any parallel plane to any coordinate planes was intersected with A is convex set . In this research we introduced a new style in the convexity is convexity in accordance with the coordinate planes ,and got a some of results and theorems, the most important : proving that every convex set in accordance with the coordinate planes is convex set, and we have offered many examples that illustrate the relationship between starshaped set, compact set , simply connected set , coordinate convex set and convex set in accordance with the coordinate planes .Downloads
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