I have a question regarding this. I wish I were home right now so I can give the exact words. Anyways, the book is talking about continuous maps from one space to another. This is basically what it says... Let f be a function with domain D in R. Then the following statements are equivalent: f is continuous If D is open, then the inverse image of every open set under f is again open. If D is closed, then the inverse image of every closed set under f is again closed. There are others, but that's not important. I just want to clarify that f does not need to be one-to-one, correct?