NORMAL THEOREM OF ALGEBROIDAL FUNCTIONS

By applying the main theorems on covering surface, a new normal criterion of algebroidal function was obtained. Let F be a family of k-valued algebroidal functions in a domain D of sphere V, and the branch points of F be isolated. If for all p\in D, there is a neighborhood U(p) such that for every f_t\in F, there exist three different complex values a_t1,a_t2,a_t3 satisfying \sum\limits_i=1^3\overlinen(U(p),a_ti,f_t)\leq 1, then F is normal in D.