On the unique range set of meromorphic functions

This paper studies the unique range set of meromorphic functions and shows that there exists a finite set S such that for any two nonconstant meromorphic functions f and g the condition E(f)(S) = E(g)(S) implies f = g. As a special case this also answers an open question posed by Gross (1977) about entire functions and improves some results obtained recently by Yi.