الاجتماع المنتهي للمجموعات النجمية في IR2
Abstract
لتكن A مجموعة كيفية في الفضاء الخطي IRn. نقول عن A إنها مجموعة نجمية إذا وجدت نقطة بحيث تكون القطعة المستقيمة محتواة في A وذلك من أجل كل .وعندئذ نقول إن النقطة x0 ترى النقطة x ضمن A (أو x مرئية من x0 ضمن A).
نثبت في هذا البحث النتيجتين التاليتين: 1- لتكن A مجموعة متراصة بسيطة الترابط في . عندئذ تكون A اجتماعاً لمجموعتين نجميتين إذا وجدت نقطتان في A مثل b,a بحيث تكون كل نقطة جبهية للمجموعة A مرئية ضمن A من إحدى النقطتين b,a (على الأقل ). 2- لتكن A مجموعة متراصة بسيطة الترابط في . عندئذ تكون A اجتماعاً لثلاث مجموعات نجمية إذا وجدت ثلاث نقاط في A مثل a,b,c بحيث تكون كل نقطة جبهية للمجموعة A مرئية ضمن A من إحدى النقاط الثلاث a,b,c (على الأقل ). Let A be a subset of the linear space IRn. We say that A is a star shaped set if a point is existed so that the segment lies in A for all In this case we say that a point x0 sees x via A (or x is seen from x0 via A). In this article we prove the following results: 1- let A be a simply connected, compact set in IR2, then A is a star shaped set if and only if there are two points a, b in A, so that all points will be seen via A at least from one of the existed points a, b. 2- let A be a simply connected, compact set in IR2, then A is a star shaped set if and only if there are three points a, b, c in A, so that all points will be seen via A at least from one of the existed points a, b, c.Downloads
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