Parusiński, Adam Lipschitz properties of semi-analytic sets. (English) Zbl 0631.32006 Ann. Inst. Fourier 38, No. 4, 189-213 (1988). 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. Cited in 32 Documents MSC: 32B20 Semi-analytic sets, subanalytic sets, and generalizations Keywords:Lipschitz stratification; semi-analytic sets; L-stratification; regular projections; L-regular sets; Lipschitz vector fields PDFBibTeX XMLCite \textit{A. Parusiński}, Ann. Inst. Fourier 38, No. 4, 189--213 (1988; Zbl 0631.32006) Full Text: DOI Numdam EuDML 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), 530-536.0435.3200681i:32003 · 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] [6] , 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. 20.0666.3201192a:32009 · 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), 555-560.0574.3201086j:32015 · Zbl 0574.32010 [9] J. L. VERDIER, Stratification de Whitney et théorème de Bertini-Sard, Invent. Math., 36 (1976), 295-312.0333.3201058 #1242 · Zbl 0333.32010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.