I am thinking if I could help with my current problem. Now I have a parameterized rational function , where denotes the coefficients (parameters) of the rational function, and denotes the indeterminate of the rational function which lies in complex domain.
I regard as a mapping from to , where is a set of rational functions with indeterminate . Then I define that a property holds on a metric space if it holds on an open dense subset of .
However, I am wondering what conditions I should put on a parameter set , such that becomes an open subset of . Is making an open dense subset of sufficient?