Singular Points of Smooth Mappings
As the notion of singular points is a purely local property the above definition can be extended to cover the wider class of smooth mappings, (functions from M to Rn where all derivatives exist). Analysis of these singular points can be reduced to the algebraic variety case by considering the jets of the mapping. The k-th jet is the Taylor series of the mapping truncated at degree k and deleting the constant term.
Read more about this topic: Singular Point Of An Algebraic Variety
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