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Level curves of open polynomial functions on the real plane |
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| Authors: | J Ferrera MJ de la Puente |
| Institution: | 1. Departamento de Análisis MatemFacultad de Matemático , Universidad Complutense , Madrid, 28040, Spain E-mail: ferrera at mat.ucm.esFacultad de Matemáticas;2. Departamento de Algebra , Universidad Complutense , Madrid, 28040, Spain E-mail: w051 at emducmll.sim.ucm.es, mpuente at mat.ucm.esFacultad de Matemáticas |
| 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. |
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