Level curves of open polynomial functions on the real plane

Abstract

Let f : f ² → R be an open polynomial function. Thenf changes sign across V(f) (alternatively around a singular point of V(f)) and the function c : R → N expressing the number f(λ) of connected components of the λ-level curve of f is lower semicontinuous; it has a removable singilarity at every value λ which is critical and is not a real critical value at infinity for f.

Partially supported by D.G.LC.Y.T. PB. 90/0044

^**Partially supported by C.I.C.Y.T. 89/0379-C02-02

Partially supported by D.G.LC.Y.T. PB. 90/0044

^**Partially supported by C.I.C.Y.T. 89/0379-C02-02

Notes

Partially supported by D.G.LC.Y.T. PB. 90/0044

^**Partially supported by C.I.C.Y.T. 89/0379-C02-02