Reading this paper http://faculty.tcu.edu/richardson/Seminars/EftonToeplitz_2016.pdf and trying to understand the Toeplitz operator's index i have found on page 4 such statement: Every nonvanishing function on $C(S^1)$ can be homotoped to $z^n$ for some $n$. I suppose that the topology on $C(S^1)$ is generated by the supremum norm. Intuitivly i understand that it's correct statement, but I can't proof this statement strick, i clearly don't understand how to find such $n$ and how to construct such homotopy, any help will be very usefull, thanks.
2026-05-16 14:34:11.1778942051
Homotopy of $f\in C(S^1)$ to $z^n$.
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