Geography and the Properties of Surfaces. The Determination of Fixed-Points in Finite-Dimensional Spaces

摘要

L.E.J. Brouwer's fixed-point theorem proves the existence of a fixed-point in a finite-dimensional space which is both convex and bounded, but provides no means of determining its position. For the case of a one-dimensional space, Marvin Shinbrot uses a graphical solution which can also be accepted as a proof for the theorem. This paper extends Shinbrot's solution to any number of dimensions. (Author)