I want to solve the following problem:
Show that the fix points of a function $f:\mathbb B^n\rightarrow \mathbb B^n$ could possibly not be in the interior. By this, Show that the Brouwer fixed-point theorem isn't true for the open ball $B_1^0 (0)$
Then we consider $n=1$ so we have the function $(x-1)/2$ in $(-1,1)$ and this proves both requirements, am I right? or what function could I use? Thanks a lot in advance.