We characterize those maps between homotopically stratified spaces whose mapping cylinders are also homotopically stratified spaces. Two applications are offered. The first concerns locally flat submanifolds of topological manifolds, and the second concerns algebraic maps between algebraic varieties.  1999 Elsevier Science B.V. All rights reserved.

If A1 is a space, the deleted product space, X*, is Xx X— D, where D is the diagonal. If y is a space and /isa continuous map from X to Y, then X* is the inverse image of Y* under the map fxf taking Xx X into Kx y. In this paper, we investigate the following questions: "What maps/are such that X* is homotopically equivalent to X*", and "What maps/are such that X* is homotopically equivalent to ...

In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...

Consider two k-gons P and Q. We say that the billiard flows in P and Q are homotopically equivalent if the set of conjugacy classes in the fundamental group of P which contain a periodic billiard orbit agrees with the analogous set for Q. We study this equivalence relationship and compare it to the equivalence relations, order equivalence and code equivalence, introduced in [BT1, BT2]. In parti...

For a closed orientable surface S, any map f : S→S whose n-th power is homotopic to the identity, is homotopic to a homeomorphism g of S of order n. This famous theorem of Nielsen is known to fail in general for aspherical manifolds. In this paper, for model aspherical manifolds M associated to a finitely extendable set of data, we, however, present a weaker version of Nielsen’s result. We show...