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Spaces of polynomials with roots of bounded multiplicity

M. GuestA. KozlowskiK. Yamaguchi — 1999

Fundamenta Mathematicae

We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by applying the "scanning method" used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.

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