WeOf knowspecial thatinterest aare those complex functionfunctions iswhich aare multiple valued functionone-to-one. That is, for distinct points ''z''{{su|b=1}}, ''z''{{su|b=2}},... in a ___domain ''D'', they may share a common value, ''f(z{{su|b=1}})''=''f(z{{su|b=2}})''=...Butonly if wethey restrictare athe complexsame functionpoint to be injective(''z''{{su|b=1}} one-one= ''z''{{su|b=2}}''), then we obtain a class of functions, viz, univalent functions. A function ''f'' analytic in a ___domain ''D'' is said to be univalent there if it does not take the same value twice for all pairs of distinct points ''z''{{su|b=1}} and ''z''{{su|b=2}} in ''D'', i.e ''f(z{{su|b=1}})''≠''f(z{{su|b=2}})'' implies ''z''{{su|b=1}}≠''z''{{su|b=2}}. Alternate terms in common use are ''schilicht'' and ''simple''. It is a remarkable fact, fundamental to the theory of univalent functions, that univalence is essentially preserved under uniform convergence.
==References==
*{{cite book |title=Geometric Function Theory: Explorations in Complex Analysis|
