The Brouwer Fixed-Point Theorem
Proof Suppose has no fixed points, i.e. for .
Define a map , , by letting be the point of intersection of and the ray starting at the point and going through . For see figure below:
with , (1)
and so is continuous. Could you please explain, in as much detail as possible, how (1) and (2) were derived?
Fixed Point Theorem and Closed Unit Ball in Euclidean Space are investigated. The solution is detailed and well presented.