In the early 1920s, Hans Reichenbach and Kurt Lewin presented two topological accounts of time that appear to be interrelated in more than one respect. Despite their different approaches, their underlying idea is that time order is derived from specific structural properties of the world. In both works, moreover, the notion of genidentity—i.e., identity through or over time—plays a crucial role. Although it is well known that Reichenbach borrowed this notion from Kurt Lewin, not much has been written about their relationship, nor about the way Lewin implemented this notion in his own work in order to ground his topology. This paper examines these two early versions of the topology of time, and follows the extent of Lewin's influence on Reichenbach's proposal.