Characterization of Minor-Closed Pseudosurfaces

A pseudosurface is obtained from a collection of closed surfaces by identifying some points. It is shown that a pseudosurface \(S\) is minor-closed if and only if \(S\) consists of a pseudosurface \(S^\circ \), having at most one singular point, and some spheres glued to \(S^\circ\) in a tree structure.