Is it possible for a multivalued complex function $f:\mathbb{C}\to\mathbb{C}$ to have an odd number of branch points?
I'm asking, as I've only seen examples of multivalued functions with an even number of branch points, but have seen no theorem or result which states that it must be such.
I believe that it must be so - that is, every multivalued function has an even number of branch points (if we include $\infty$ too, if that turns out to be a branch point). My reasoning is that if not, then we would not be able to define a branch cut between $2$ branch points. However, I've not been able to show this rigurously.