  We study the structure induced on a smooth manifold by a continuous selection
of smooth functions. In case such selection is suitably generic, it provides a
stratification of the manifold, whose strata are algebraically defined smooth
submanifolds. When the continuous selection has nondegenerate critical points,
stratification descends to the local topological structure. We analyze this
structure for the maximum of three smooth functions on a 4-manifold, which
provides a new perspective on the theory of trisections.
