Detecting codimension one manifold factors with 0-stitched disks

The 0-stitched disks property is introduced and shown to detect codimension one manifold factors of dimension n ⩾ 4 . It is shown that if a space X is an ANR and has the 0-stitched disks property, then X has the disjoint homotopies property. It follows that if a space X is a resolvable generalized manifold of dimension n ⩾ 4 with the 0-stitched disks property, then X is a codimension one manifold factor. Whether or not the 0-stitched disks property is equivalent to the disjoint homotopies property remains an open question.