  Graphons are analytic objects associated with convergent sequences of dense
graphs. Finitely forcible graphons, i.e., those determined by finitely many
subgraph densities, are of particular interest because of their relation to
various problems in extremal combinatorics and theoretical computer science.
Lovasz and Szegedy conjectured that the topological space of typical vertices
of a finitely forcible graphon always has finite dimension, which would have
implications on the minimum number of parts in its weak eps-regular partition.
We disprove the conjecture by constructing a finitely forcible graphon with the
space of typical vertices that has infinite dimension.
