On semi-analytic and subanalytic geometry
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Every semianalytic set admits a semianalytic stratification, i.e. a stratification consisting of semianalytic strata only.
“Moreover, it can be shown [21,28] that every semianalytic set admits a semianalytic stratification, i.e., a stratification consisting of semianalytic strata only.”
From Representations of the Weyl Algebra in Quantum Geometry (2009) · cites this paper as [28]
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Cites
Schwartz, L. (1966) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 3,541 · see citing works
Singular points of complex hypersurfaces
Milnor, J. (1968) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 2,296 · see citing works
Semianalytic and subanalytic sets
Bierstone, E., & Milman, P. D. (1988) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02699126 · Cited by 671 · see citing works
Ideals of differentiable functions
Malgrange, B. (1966) · Medical Entomology and Zoology · Cited by 660 · see citing works
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Self-citationTriangulation of semi-analytic sets
Łojasiewicz, S. (1964) · French digital mathematics library (Numdam) · Cited by 365 · see citing works
Self-citationIntroduction to Complex Analytic Geometry
Łojasiewicz, S. (1991) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-7617-9 · Cited by 331 · see citing works
Self-citationOn the division of distributions by polynomials
Hörmander, L. (1958) · Arkiv för matematik · doi:10.1007/bf02589517 · Cited by 251 · see citing works
Stratifications de Whitney et théorème de Bertini-Sard
Verdier, J.-L. (1976) · Inventiones mathematicae · doi:10.1007/bf01390015 · Cited by 234 · see citing works
Projections of semi-analytic sets
Gabrielov, A. M. (1968) · Functional Analysis and Its Applications · doi:10.1007/bf01075680 · Cited by 161 · see citing works
Lipschitz stratification of subanalytic sets
Parusiński, A. (1994) · Annales Scientifiques de l École Normale Supérieure · doi:10.24033/asens.1703 · Cited by 99 · see citing works
Triangulation of subanalytic sets and proper light subanalytic maps
Hardt, R. (1976) · Inventiones mathematicae · doi:10.1007/bf01403128 · Cited by 94 · see citing works
Introduction to real-analytic sets and real-analytic maps
広中, 平. (1973) · Medical Entomology and Zoology · Cited by 92 · see citing works
Subanalytic sets in the calculus of variation
Tamm, M. (1981) · Acta Mathematica · doi:10.1007/bf02392462 · Cited by 66 · see citing works
Lipschitz properties of semi-analytic sets
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Points réguliers d'un sous-analytique
Kurdyka, K. (1988) · Annales de l’institut Fourier · doi:10.5802/aif.1126 · Cited by 22 · see citing works
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Research works printed but not linked: 23
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- Triangulation of algebraic sets, Proceedings of Symp. in Pure Math., vol. 29 (1975).
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- J. S t a s i c a, The Whitney condition for subanalytic sets, Zesz. Nauk. U.J., Prace Mat. 32 (1982), pp. 211-221.
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Sorted by citations
Representations of the Weyl Algebra in Quantum Geometry
Fleischhack, C. (2009) · Communications in Mathematical Physics · doi:10.1007/s00220-008-0593-3 · Cited by 183 · see citing works
- Authors
- Łojasiewicz, S.
- Affiliations
- Jagiellonian University (PL)
- Corresponding author
- Łojasiewicz, Stanisław
- Venue
- Banach Center Publications
- Published
- 1995
- Volume
- 34
- Issue
- 1
- Pages
- 89-104
- ISSN
- 0137-6934 (ISSN-L)
- 1730-6299
- OpenAlex
- W1009385846
- Cited by
- 43
- References
- 19
- Citations by year
- 2024: 1 · 2023: 2 · 2022: 1 · 2021: 3 · 2020: 5 · 2019: 1 · 2016: 1
- FWCI
- 0.63
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Banach Center Publications (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Topology and Set Theory
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical and Theoretical Analysis
- Keywords
- subanalytic sets, real analytic geometry, o-minimality, definable sets
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