CONTENTS 1. Introduction and statement of the results........................5 2. Lipschitz vector fields and stratifications.........................9 3. Generalized normal partitions.......................................10 4. Regular projections.......................................................13 5. Quasi-wings..................................................................17 A. Selection of quasi-wings..............................................18 B. Lifting of quasi-wings...................................................18 C. Nicely situated quasi-wings..........................................19 D. Tangent spaces to nicely situated quasi-wings............22 6. Proof of Proposition 1.2................................................23 7. Whitney's conditions.....................................................29 8. Extended quasi-wings...................................................31 9. Proof of Proposition 1.3................................................35 10. Proof of Proposition 1.4..............................................40 Bibliography......................................................................46
[1] S. Akbulut, H. C. King, The topology of a real algebraic set with isolated singularities, Ann. of Math. 113 (1981), 425-466.
[2] S. Banach, Wstęp do teorii funkcji rzeczywistych, Monografie matematyczne, Warszawa-Wrocław 1951.
[3] J. Briancon, J. P. Speder, La trivialité topologique n'implique pas les conditions de Whitney, C. R. Acad. Se. Paris, t. 280, serie A (1975), p. 365.
[4] Z. Denkowska, S. Łojasiewicz, J. Stasica, Certaines propriétés élémentaires des ensembles sous-analytiques, Bull. Acad. Polon. Sci. 27 (1979), 530-536.
[5] P. Griffiths, Complex differential and integral geometry ..., Duke Math. J. 45 (1978), 427-512.
[6] S. Lang, Algebra, Addison-Wesley Publishing Company, Reading, Mass. 1965.
[7] S. Łojasiewicz, Ensembles semi-analytiques, IHES 1965.
[8] J. N. Mather, Stratifications and mappings, Dynamical systems, Academic Press, New York 1973.
[9] A. N. Varčenko, Teoremy topologiceskoj ekwisingularnosti ..., Izv. Akad. Nauk CCCP 36 (1972), 957-1019.
[10] J. L. Verdier, Stratifications de Whitney et théorème de Bertini-Sard, Invent. Math. 36 (1976), 295-312.
[11] C. T. C. Wall, Regular stratifications in: Dynamical systems, Warwick 1974, Lecture Notes in Mathematics 468, Springer-Verlag, Berlin 1975, p. 332-344.