A look at the single-valuedroot function of Riemann

Abstract: We study aspects of the multivalued complex root function and considerthree different ways to construct topological spaces where it becomes singlevalued.For each topological space created, we show that there exists homeomorphismsto the unit sphere. A generalisation is given (Theorem 6.1.4)which can be used to create new domains to multivalued inverses for continuousfunctions. We compare the different ways to create the domains astopological spaces together with their single-valued functions.