The study of technology and technological change is a dynamic field where diverse disciplines from the social sciences and the humanities converge. It is possible to find several ontologies that incorporate topological referents as heuristic metaphors and simple methodological devices in technological studies. The paper examines two related topological concepts, continuity and convergence, based on the notions of accumulation of knowledge and a combination of pre-existing technologies to arrive at the notions of convergence and inflation. The paper concludes with some future research guidelines that formally explore the potential of topology in technology and technological change studies.