2-ghastly spaces with the disjoint homotopies property: The method of fractured maps

Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

“…There are also several related general position properties that fall into subclasses of these properties. For example, spaces that have the plentiful 2-manifolds property [11], the 0-stitched disks properties [13], or for which the method of δ-fractured maps can be applied [12], all have the disjoint homotopies property. The crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property all imply the disjoint topographies property [14].…”

Decompositions of $${\mathbb {R}^n, n \ge 4}$$ , into Convex Sets Generate Codimension 1 Manifold Factors

“…For resolvable generalized manifolds, we have the following very useful approximate lifting theorem, which follows from [11, Theorem 17.1 and Corollary 16.12B]: General position properties are very useful in detecting codimension one manifold factors [12,16,17,18,20]. For our results, we shall only need to employ the following:…”

Detecting codimension one manifold factors with topographical techniques

“…• The disjoint arc-disk property [2] • The disjoint homotopies property [11] -The plentiful 2-manifolds property [10] -The method of δ-fractured maps [10] -The 0-stitched disks property [11] • The disjoint concordances property [5] It should be noted here that the disjoint concordances property is the only property listed that provides a characterization of codimension one manifold factors. Specifically, a resolvable generalized manifold X of finite dimension n ≥ 4 is a codimension one manifold factor if and only if X satisfies the disjoint concordances property.…”