  We develop a theory of tubular neighborhoods for the lower strata in manifold
stratified spaces with two strata. In these topologically stratified spaces,
manifold approximate fibrations and teardrops play the role that fibre bundles
and mapping cylinders play in smoothly stratified spaces. Applications include
the classification of neighborhood germs, the construction of exotic
stratifications, a multiparameter isotopy extension theorem and an h-coborsism
extension theorem.
