Abstract:In this work we approach the problem of determining which (compact) semialgebraic subsets of R n are images under polynomial maps f : R m → R n of the closed unit ball Bm centered at the origin of some Euclidean space R m and that of estimating (when possible) which is the smallest m with this property. Contrary to what happens with the images of R m under polynomial maps, it is quite straightforward to provide basic examples of semialgebraic sets that are polynomial images of the closed unit ball. For instanc… Show more
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