Note: I have many questions and will keep posting new ones as they come up. To find the questions simply scroll down to look for bold segments. Feel free to contribute any other comments relevant to the questions or the topic itself. Here it is... Let p:E->B be continuous and surjective. Suppose that U is an open set of B that is evenly covered by p. Show that if U is connected, then the partition of p^(-1)(U) into slices is unique. Ok, I barely understand what it's asking me to show. Is it saying the partition of p^(-1)(U) is unique? Because I highly doubt it's that because any set can be partitioned many different ways! I think it's saying that if we have a map p1:E->B that is continuous and surjective and that U is evenly covered by p1, then the partition p1^(-1)(U) will be the same as p^(-1)(U). Is that it?