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Building on fields of inquiry in mathematics and computer science, the terms topology and network topologies may offer urban studies a way to think about globalization, policy mobility, and the emergence of a middle class. Topology is a part of mathematics that addresses the consistency of properties even with shifts in size or shape of a figure – for instance with the “stretching” or “bending” (but not the breaking or tearing) of a figure – and thus has been helpful for thinking about what is generalizable across disparate cases and what is not. Topology and topological spaces have been taken up by geographers, anthropologists, and urbanists to think about spatiality, relationality and connectivity, generalizations developed through comparison, and assemblages. In this paper, I consider what we gain by thinking “with topology” – especially for issues of urban innovation and the emergence of new forms of social distinctions, in particular the middle class.

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