Ross Kang

1 Introduction A common refrain in combinatorics is that once you have one, you have many—that is to say, combinatorial objects of a desired structure. The phenomenon, going back at least to unpublished work in 1941 of Rademacher (see Erdős 1955), is referred to as supersaturation and may be observed in many, especially extremal, combinatorial contexts. We pursue a similar line that, rather than multitude, asks instead for topological structure in the space of desired combinatorial objects.