Many disentanglement methods represent generative factors using Euclidean product coordinates, although the underlying factor spaces may wrap, collapse, or have position-dependent geometry. We introduce factor-space structure, which combines factor domains, generator-induced identifications, and position-dependent scales to distinguish topologically equivalent spaces with different factor geometries. We show that statistical independence does not imply uniform product geometry: independent hue and scale can affect observations at different, scale-dependent rates, producing anisotropy that no fixed rescaling can remove. We propose the Factor-Space Topographic Map (FactoMap), which learns interpretable prototypes indexed by a structured factor-space lattice. Topographic learning transfers the lattice's periodicity, collapses boundaries, and non-uniform extent to the representation. Experiments show that matching this structure better preserves factor continuity and improves disentanglement of the underlying factors.

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