I just recently started a chapter on elementary multi-valued functions of a complex variable, and one part of the book text a bit confuses me. To give a little context, the segment covers branch points and how to define them; in that specific case we learn that ∞ (infinity) is a branch point of the nth root of a polynomial. Now, the text says that given a neighborhood of infinity which does not contain any roots of the polynomial, there is a Jordan Curve which belongs to the neighborhood of infinity and whose exterior contains the point at infinity. The problem I am having is that the book then tells me that the interior of that very Jordan Curve, on the other hand, does contain all those roots. But, if the Jordan curve is a subset of a neighborhood which does not contain any roots, how can its interior have all of them?
For more clarity, here is this paragraph from the book: (you can ignore the last sentence)
Thank You!!!