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Lipschitz properties of semi-analytic sets. (English) Zbl 0631.32006
The existence of Lipschitz stratification, in the sense of Mostowski, for compact semi-analytic sets is proved. (This stratification ensures the constance of the Lipschitz type along each stratum). The proof is independent of the complex case, considered by Mostowski, and gives also some other Lipschitz properties of semi-analytic sets.

##### MSC:
 32B20 Semi-analytic sets, subanalytic sets, and generalizations
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##### References:
 [1] S. BANACH, Wstep do teorii funkcji rzeczywistych, Monografie Matematyczne, Warszawa-Wroclaw, 1951. [2] Z. DENKOWSKA, S. LOJASIEWICZ, J. STASICA, Certaines propriétés élémentaires des ensembles sous-analytiques, Bull. Pol. Acad. Sci. (Math), Vol. 27, N° 7-8 (1979), 530-536. · Zbl 0435.32006 [3] H. HIRONAKA, Introduction to real-analytic sets and real-analytic maps, Inst. Mat. “L. Tonelli”, Pisa, 1973. [4] S. LOJASIEWICZ, Ensembles semi-analytiques, Inst. Hautes Sci. Publ. Math., Paris, 1965. · Zbl 0241.32005 [5] J. MATHER, Stratifications and mappings, Proc. Dynamical Systems Conference, Salvador, Brazil, 1971, Acad. Press. · Zbl 0286.58003 [6] T. MOSTOWSKI, Lipschitz equisingularity, Dissertationes Math., 243 (1985). · Zbl 0578.32020 [7] A. PARUSIŃSKI, Lipschitz stratification of real analytic sets, to appear in “Singularities”, Banach Center Publ., Vol. 20. · Zbl 0666.32011 [8] W. PAWLUCKI, Le théorème de Puiseux pour une application sous-analytique, Bull. Pol. Acad. Sci. (Math), Vol. 32, N° 9-10 (1984), 555-560. · Zbl 0574.32010 [9] J. L. VERDIER, Stratification de Whitney et théorème de Bertini-sard, Invent. Math., 36 (1976), 295-312. · Zbl 0333.32010
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