For every p∈M there exists a neighborhood U of p with the following property: If q∈M∩U and (X,q) is a germ of a complex subvariety such that (X,q)⊂(M,q), t...For every p∈M there exists a neighborhood U of p with the following property: If q∈M∩U and (X,q) is a germ of a complex subvariety such that (X,q)⊂(M,q), then there exists a complex subvariety Y⊂U (in particular a closed subset of U) such that Y⊂M and (X,q)⊂(Y,q).