Contents Introduction ix I. Preliminaries 1 §1. General Definitions 1 §2. The HilbertCube. 1 §3. Z-Sets 2 §4. Proper Maps 4 §5. A Convergence Criterion 4 Notes 6 II. Z-Setsin Q . 7 §6. Infinite Codimension . . . . . . . . . . . . . . . . . . . . . 7 §7. Extending Homeomorphisms 9 §8. Approximating Maps by Embeddings 10 §9. Estimated Extensions of Homeomorphisms . . . . . . . . . . . . 11 §10. Homeomorphing Z-sets into s 12 §11. The Main Results. 14 §12. Some Applications . 14 Notes 17 III. Stability of Q-Manifofds 18 §13. Open Subsets of Q 18 §14. Variable Products 20 §15. The Main Result 22 Notes 24 IV. Z-Sets in Q-Manifolds 25 §16. Collared Submanifolds 25 §17. Reduction to Q 25 §18. Approximating Maps by Z-Embeddings 27 §19. Extending Homeomorphisms 28 Notes 31 V. Q-Manifolds of the Form M x [0,1) 32 §20. Engulfing. 32 §21. The Main Result 33 §22. Compact Contractible Q-Manifolds 35 §23. Triangulating Q-Manifolds 36 Notes 38 VI. Shapes of Z-Sets in Q . . 39 §24. Borsuk's Definition of Shape 39 §25. The Complement Theorem 39 Notes 44 VII. Near Homeomorphisms and the Sum Theorem 45 §26. Near Homeomorphisms 45 §27. The Sum Theorem 47 Notes 53 VII
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