Teardrops are generalizations of open mapping cylinders. We prove that the teardrop of a stratified approximate fibration X → Y ×R with X and Y homotopically stratified spaces is itself a homotopically stratified space (under mild hypothesis). This is applied to manifold stratified approximate fibrations between manifold stratified spaces in order to establish the realization part of a previous...

The first disentanglement of a multigerm f : (‫ރ‬ 2n , S) → (‫ރ‬ 3n , 0) is shown to be homotopically equivalent to a wedge of (n+1)-spheres and 2-spheres. For corank-1 monogerms in the same dimensions, the second disentanglement is shown to be homotopically equivalent to a wedge of n-spheres and circles. Good real perturbations of such maps are investigated and it is shown for multigerms in th...

The algebraic as well geometric topological constructions of manifold embeddings and homotopy offer interesting insights about spaces symmetry. This paper proposes the construction 2-quasinormed variants locally dense p-normed 2-spheres within a non-uniformly scalable quasinormed (C, R) space. fibered space is are equivalent to category 3-dimensional manifolds or three-manifolds with simply con...