The notion of legal space is increasingly being used to address the challenges of multiple and overlapping spheres of legality that the notion of legal order cannot capture. This article shows how legal space can serve as an alternative (or at least complementary) concept to legal order in view of the limitations of the latter. It sketches out a notion of legal space that is inspired by topology, an approach that analyses the qualitative nature of spaces. It is concerned with understanding the ways in which legalities interact, rather than with ‘measuring’ their spatial dimensions. A topology-inspired approach to legal space can contribute to conceptualizing, in a novel manner, the inner structure of legal spaces, the boundaries of these spaces and their interrelations with other spaces. It offers an analytical toolkit for better understanding multiple legalities, providing categories to characterize sets of legal elements as well as phenomena such as overlaps and hybridity. It is conceptually less constrained than the concept of legal order, and thus allows us to address various bodies of law ranging from classical domestic law, EU law and international law to global administrative law, corporate social responsibility law, platform law and lex sportiva.