Machine knitted textiles are complex multi-scale material structures increasingly important in many industries, including consumer products, architecture, composites, medical, and military. Computational modeling, simulation, and design of industrial fabrics require efficient representations of the spatial, material, and physical properties of such structures. We propose a process-oriented representation, TopoKnit, that defines a foundational data structure for representing the topology of weft-knitted textiles at the yarn scale. Process space serves as an intermediary between the machine and fabric spaces, and supports a concise, computationally efficient evaluation approach based on on-demand, near constant-time queries. In this paper, we define the properties of the process space, and design a data structure to represent it and algorithms to evaluate it. We demonstrate the effectiveness of the representation scheme by providing results of evaluations of the data structure in support of common topological operations in the fabric space.