Brouwer fixed point theorem. However, here it is (0,1] hence take .
Trying to figure out these two questions, got the rest of them but can't remember my linear algebra for the life of me thanks!
a. make a continuous function (0,1] --> (0,1] without fixed points.
note: there is supposed to be some simple map but honestly I can't see it.
b. prove that the unit square [0,1]x[0,1] is homeomorphic to the parellelogram in Rē with vertices (3,2), (6,5), (4,4), and (7,7). Use a suitable map and an appropriate translation.
Thanks so much for the help appreciated.