Darboux's monodromy theorem

Darboux's monodromy theorem

[′där·büz ¦män·ə‚drä·mē ‚thir·əm]
(mathematics)
The proposition that, if the function ƒ(z) of the complex variable z is analytic in a domain D bounded by a simple closed curve C, and ƒ(z) is continuous in the union of D and C and is injective for z on C, then ƒ(z) is injective for z in D.