# What the meaning of "generic" in Colding-Minicozzi's paper "Generic mean curvature flow I; generic singularities"?

What is the exact meaning of "generic" in Colding-Minicozzi's paper "Generic mean curvature flow I; generic singularities"? (DOI link, arXiv link) Is there a specific explanation somewhere? I did not find it in that paper. Does someone know a paper or a book having a expanation of it? Thanks.

• It appears they are using it in the sense of general position. i.e. a feature of a metric is "generic" if it also holds for all nearby metrics. Apr 19 at 18:47

Thus the question is what topology they are using here. For the space of hypersurfaces, it usually means the $$C^\infty$$-topology, that is, locally they could be written as graphs and they converge in any $$C^k$$-norm.