Studies on technological innovation systems (TISs) often set spatial boundaries at the national level and treat supranational levels as a geographically undifferentiated and freely accessible global technological opportunity set. This article criticizes this conceptualization and proposes instead to analyze relevant actors, networks and processes in TIS from a relational perspective on space. It develops an analytical framework which allows investigating innovation processes (or 'functions') of a TIS at and across different spatial scales. Based on social network analysis of a co-publication dataset from membrane bioreactor technology, we illustrate how the spatial characteristics of collaborations in knowledge creation vary greatly over relatively short periods of time. This finding suggests that TIS studies should be more reflexive on system boundary setting both regarding the identification and analysis of core processes as well as in the formulation of policy advice.