استخدام التقسيم النظامي للسيمبلكس النوني القياسي في إثبات مبرهنة بروور للنقطة الثابتة

The Brouwer Fixed Point Theorem is one of the very well–known theorems in mathematics. It is a generalization of the Intermediate-Value Theorem. It also has many proofs. First, we prove that if is a standard simplex in , and we have a continuous function from to itself, then, by using the standard division of the standard n–simplex, this function has at least one fixed point. Then, we prove that any compact convex subset in has the property of the fixed point.