I want to define a function ```g[s]``` such that ```g[s_]:=f[s]``` in a (arbitrarily small open) neighborhood around ```s1``` and ```g[s_]:=0``` in a (arbitrarily small open) neighborhood around ```s2```.

How do I do that?  It looks like Piecewise requires actual numbers to be inputted, but I don't have numerical values of ```s1``` and ```s2```, so I don't think I can use that.

The goal would be to get it so that, for example,
```
Derivative[n][g][s1]==Derivative[n][f][s1]
Derivative[n][g][s2]==0
```