Social media are said to offer seemingly endless ways of connecting with people in a variety of online spaces. The mediated form that such communication takes has re-opened many theoretical debates regarding the status of relationships that are organized and managed online. In this article we seek to explore these issues through the lens of topological thinking, and particularly through the work of Kurt Lewin (1890–1947). Lewin’s topological psychology has recently featured in the social sciences as a way of overcoming some of the, frankly unhelpful, dualistic thinking that features commonly in psychology (e.g. subject–object, mind–body, individual–social). Topological thought focuses on the spatial distribution of psychological experience, and therefore offers a social perspective not reliant on traditional notions of internalized psychological states and traits. The kind of spatiality at work though is not one that relies on Euclidean fixity, but one that draws out notions of stretching, moulding, bending and flexing. Space is seen not as a fixed property, but rather the form that psychological activity takes through connections and relations with others. In this article we seek to explore the potential value in characterizing social media activity topologically. This involves analysing people’s experiences with social media, and how topological concerns of boundaries, connections and thresholds work (or not) in and through social media. Furthermore, the focus is not only on extensive properties of social media, but rather on how intensive processes are actualized and distributed in and through mediation.