Objects’ topological properties play a central role in object perception, superseding objects’ surface features in object representation and tracking from early in development. We asked about the role of objects’ topological properties in children’s generalization of novel labels to objects. We adapted the classic name generalization task of Landau et al. ( 1988 , 1992 ). In three experiments, we showed children ( n = 151; 3–8-year-olds) a novel object (the standard) and gave the object a novel label. We then showed children three potential target objects and asked children which of the objects shared the same label as the standard. In Experiment 1, the standard object either did or did not contain a hole, and we asked whether children would extend the standard’s label to a target object that shared either metric shape or topology with the standard. Experiment 2 served as a control condition for Experiment 1. In Experiment 3, we pitted topology against another surface feature, color. We found that objects’ topology competed with objects’ surface features (both shape and color) in children’s extension of labels to novel objects. We discuss possible implications for our understanding of the inductive potential of objects’ topologies for making inferences about objects’ categories across early development.