Ordnungseigenschaften holomorpher Funktionen

A linear geometric order theory for holomorphic mappings F: ^nm is given if a family of linear subspaces L of ⁿ×^m is specified; the theory then is concerned with the order number of connected parts of the intersections L (F) of the L's with the graph (F) of F. For m=1 (i.e. case of one function) it is proved that the local linear order number of a holomorphic function is finite in every point. If the L's are real-linear subspaces then real differential geometric methods lead to the proof, if the L's are complex-linear then ideal-theoretical means do.