Geodesic
Local topological properties of analytic mappings
Izvestiya. Mathematics , Tome 7 (1973) no. 4, pp. 883-917.

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In this paper one studies the local topological structure of analytic mappings. It is proved that the complement in the space of all germs of analytic mappings from $\mathbf C^n$ to $\mathbf C^q$ of the set of germs whose topological type is unchanged under alteration of large terms of the Taylor series has infinite codimension. 
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A. N. Varchenko. Local topological properties of analytic mappings. Izvestiya. Mathematics , Tome 7 (1973) no. 4, pp. 883-917. http://geodesic.mathdoc.fr/item/IM2_1973_7_4_a6/

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