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In many articles about topology, Reeb space etc. I came accross the term generic map, or generic smooth map but I haven't found any definition of such "genericity"... could you help me ?

Example of use from https://pdfs.semanticscholar.org/36ea/f7d4db2653769b39ff7927c38e812f3eba87.pdf :

We study the local and global structure of this space for generic, piecewise linear mappings on a combinatorial manifold.

hl037_
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  • I believe generic is being used literally here, in place of "any". It indicates generality. – The Count May 13 '17 at 19:22
  • It ordinarily signifies a dense (often open, too) set of mappings in an appropriate topology on the space of mappings. – Ted Shifrin May 13 '17 at 19:24
  • @The Count I'm not sure : in http://www.ee.oulu.fi/research/imag/courses/Vaccarino/Edels_Book.pdf , Edelsbruner dedicate a part aoubt "generic maps" where he says that smooth mappings enough to "tame" mappings on manifold, while "generics mapping" does... However, I haven't seen any formal definition of his "genericity" – hl037_ May 13 '17 at 19:28
  • In the case of this specific example, the definition is given right in the article you linked, in the second paragraph of the "background" section: "[w]e call $f$ a generic PL mapping if the images of the vertices have no structural properties that can be removed by arbitrarily small perturbations of the vertex map." – A.P. May 13 '17 at 20:10

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