Abstract: Butterfield (2011) has recently presented a case for the compatibility of reduction and emergence in some of the exact sciences. He takes reduction to be given by one theory being the limit of another, and emergence to be "novel and robust behavior" arising "on the way to the limit." Here I aim to make this idea more precise, emphasizing the necessary role of similarity relations between the models of the two theories, encoded formally by a choice of topology on them. I stress that justifying why a notion of similarity is appropriate is crucial, as it may perform much of the work in demonstrating a particular reduction's success or failure, and in explicating the sense of "novel and robust behavior" of a candidate emergent property. To illustrate, I consider the case of gravitational theory, and the emergence of features like "objective simultaneity".