On the Intermediate Point Principle
キーワード:
The intermediate point principle,
the intermediate value theorem,
the Brouwer fixed point theorem,
Poincaré–Miranda’s theorem
2022 年 1 巻 p. 17-22
詳細
2022 年 1 巻 p. 17-22
In the Euclidean space of all real numbers, we know that the Brouwer fixed point theorem and Poincaré–Miranda’s theorem are derived directly from the intermediate value theorem. So, Brouwer’s theorem is a partial extension of the intermediate value theorem. Then, in this note, we prove an extension of the intermediate value theorem itself in the n-dimensional Euclidean space. Maybe it should be called the intermediate point principle.
