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A fixed-point theorem is a result saying that a function $F$ will have at least one fixed point (a point $x$ for which $F(x) = x$), under some conditions on $F$ that can be stated in general terms.

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Has the Fundamental Theorem of Algebra been proved using just fixed point theory?

Question: Is there already in the literature a proof of the fundamental theorem of algebra as a consequence of Brouwer's fixed point theorem? N.B. The original post contained superfluous inform …