Neighborhoods in stratified spaces with two strata

We develop a theory of tubular neighborhoods for the lower strata in manifo ld stratified spaces with two strata, In these topologically stratified spa ces, manifold approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applicat ions include the classification of neighborhood germs, a multiparameter iso topy extension theorem and an h-cobordism extension theorem. (C) 2000 Elsev ier Science Ltd, All rights reserved. MSG: primary 57N80; 57N40; 57R80; sec ondary 19J99; 55R65; 57N40.