Fact Suppose E C is open, and f is a function from E to C. Then f is continuous if and only if the following property holds: f 1(U) is an open subset of E whenever U is open. A multi-valued …

Multivalued Functions Introduced as the inverse of single valued functions, eg. z = !2 Inverting above, yields the simplest multivalued function

multivalued function. Riemann surfaces depend on the funct on being investigated. We now give a nontechnical formulation of the Riemann surface for the multivalue

To use multivalued functions, one must pick out a branch in some region R where the functions is single-valued and continuous. This is done with cuts and Riemann sheets.

For a multiple-valued function, a branch is a choice of range for the function. We choose the range to exclude all but one possible value for each element of the domain.

Jan 6, 2022 · ame point . Def. A branch point of a multivalued function is one where upon traversing a small circle around the point, the value of the function does not return

Multivalued functions. Let q; m; n 1 be integers and Rm. A q-valued function is a map : u ! Aq(Rn). We will represent a q-valued function u as q X u(x) = ui(x)