A local interior-exterior distinction is formulated for matching across a hypersurface, and detailed examples are given for spherical dust flows. While the "inside" vs "outside" character is not, in general, globally preserved, the distinction is unambiguous in an $\mathcal{R}$ region, and does afford clarification of certain boundary surfaces and surface densities discussed in the literature.

• Received 8 July 1977

DOI:https://doi.org/10.1103/PhysRevD.17.1935