zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Homology theory for real analytic and semianalytic sets. (English) Zbl 0309.32004

MSC:
32B20Semi-analytic sets; subanalytic sets
32C05Real-analytic manifolds and spaces
55N35Other homology theories (algebraic topology)
55N45Products and intersections (algebraic topology)
WorldCat.org
Full Text: Numdam EuDML
References:
[1] A. Borel - A. Haefliger , La classe d’homologie fondamentale d’un espace analytique , Bull. Soc. Math. France , 89 ( 1961 ), pp. 461 - 513 . Numdam | MR 149503 | Zbl 0102.38502 · Zbl 0102.38502 · numdam:BSMF_1961__89__461_0 · eudml:87009
[2] Eilenberg - N. Steenrod , Foundations of algebraic topology , Princeton University Press , Princeton , 1952 . MR 50886 | Zbl 0047.41402 · Zbl 0047.41402
[3] H. Federer , Geometric measure theory , Springer-Verlag , Heidelberg and New York , 1969 . MR 257325 | Zbl 0176.00801 · Zbl 0176.00801
[4] B. Giesecke , Simplicial Zerlegung abzähbahlbarer analytische raüme , Math. Zeit. , 83 ( 1964 ), pp. 177 - 213 . MR 159346 | Zbl 0123.39602 · Zbl 0123.39602 · doi:10.1007/BF01111199 · eudml:170224
[5] L. Grauert , On Levi’s problem and the embedding of real analytic manifolds , Ann. of Math. , 68 ( 1958 ), pp. 460 - 472 . MR 98847 | Zbl 0108.07804 · Zbl 0108.07804 · doi:10.2307/1970257
[6] R.M. Hardt , Slicing and intersection theory for chains associated with real analytic varieties , Acta Math. , 129 ( 1972 ), pp. 75 - 136 . MR 315561 | Zbl 0234.32005 · Zbl 0234.32005 · doi:10.1007/BF02392214
[7] R.M. Hardt , Slicing and intersection theory for chains modulo é associated with real analytic varieties , Trans. Amer. Math. Soc. , 183 ( 1973 ), pp. 327 - 340 . MR 338430 | Zbl 0267.28010 · Zbl 0267.28010 · doi:10.2307/1996472
[8] R.M. Hardt , Stratification of real analytic mappings and images , Inventiones Math. 28 ( 1975 ), pp. 193 - 208 . MR 372237 | Zbl 0298.32003 · Zbl 0298.32003 · doi:10.1007/BF01436073 · eudml:142321
[9] J.L. Kelley , General Topology , Van Nostrand , New York , 1955 . MR 70144 | Zbl 0066.16604 · Zbl 0066.16604
[10] B.C. Koopman - A.B. Brown , On the covering of analytic loci by complexes , Trans. Amer. Math. Soc. , 34 ( 1932 ), pp. 231 - 251 . MR 1501636 | Zbl 0004.13203 | JFM 58.1203.02 · Zbl 0004.13203 · doi:10.2307/1989540 · http://www.emis.de/cgi-bin/JFM-item?58.1203.02
[11] S. Lojasiewicz , Sur le problème de la division , Rozprawy Mathematyczne , no. 22 , Warsaw , 1961 . MR 126072 | Zbl 0096.32102 · Zbl 0096.32102
[12] S. Lojasiewicz , Triangulation of semi-analytic sets , Annali Sc. Norm. Sup. Pisa , serie 3 , 18 ( 1964 ), pp. 449 - 474 . Numdam | MR 173265 | Zbl 0128.17101 · Zbl 0128.17101 · numdam:ASNSP_1964_3_18_4_449_0 · eudml:83333
[13] S. Lojasiewicz , Ensembles semianalytiques, Cours Faculté des Sciences d’Orsay , I.H.E.S ., Bures-sur-Yvette , 1965 .
[14] S. Lojasiewicz , Une propriété topologique des sous-ensembles analytique reéls, Colloques internationaux du Centre National de la Recherche Scientifique, no. 117 , Les Equations aux Dérivées Partielles , Paris , 1962 , pp. 87 - 89 . MR 160856 | Zbl 0234.57007 · Zbl 0234.57007
[15] R. Narashimhan , Introduction to the theory of analytic spaces , Springer-Verlag , New York , 1966 . Zbl 0168.06003 · Zbl 0168.06003 · doi:10.1007/BFb0077071
[16] A. Seidenberg , A new decision method for elementary algebra , Ann. of Math. , 60 ( 1954 ), pp. 365 - 374 . MR 63994 | Zbl 0056.01804 · Zbl 0056.01804 · doi:10.2307/1969640
[17] E.H. Spanier , Algebraic topology , McGraw-Hill , New York , 1966 . MR 210112 | Zbl 0145.43303 · Zbl 0145.43303
[18] R. Thom , Ensembles morphismes stratifiés , Bull. Amer. Math. Soc. , 75 ( 1969 ), pp. 240 - 284 . Article | MR 239613 | Zbl 0197.20502 · Zbl 0197.20502 · doi:10.1090/S0002-9904-1969-12138-5 · http://minidml.mathdoc.fr/cgi-bin/location?id=00221039
[19] B.L. Van Der Waerden , Algebra , vol. 1 , Ungar , New York , 1970 .
[20] H. Whitney , Geometric integration theory , Princeton University Press , Princeton , 1957 . MR 87148 | Zbl 0083.28204 · Zbl 0083.28204
[21] ] H. H , Subanalytic sets, Numer Theory, Algebraic Geometry, and Commutative Algebra (Dedicated to Akizuki) , Kinokunia , Tokyo , 1973 , pp. 453 - 493 . MR 377101 | Zbl 0297.32008 · Zbl 0297.32008
[22] H. Hironaka , Introduction to real analytic sets and real analytic maps , Lecture notes of Istituto matematico Leonida Tonelli , Pisa , 1973 . MR 477121
[23] D. Sullivan , Combinatorial invariants of analytic spaces, Proceedings of Liver-pool Singularities-Symposium I , Springer-Verlag Lecture Notes in Mathematics , 192 ( 1971 ), pp. 165 - 168 . MR 278333 | Zbl 0227.32005 · Zbl 0227.32005
[24] D. Burghelea - A. Verona , Local homological properties of analytic sets , Manuscripta Math. , 7 ( 1972 ), pp. 55 - 62 . MR 310285 | Zbl 0246.32007 · Zbl 0246.32007 · doi:10.1007/BF01303536 · eudml:154106
[25] R.M. Hardt , Sullivan’s local Euler characteristic theorem , Manuscripta Math. , 12 ( 1974 ), pp. 87 - 92 . MR 338431 | Zbl 0281.32005 · Zbl 0281.32005 · doi:10.1007/BF01166236 · eudml:154229
[26] R.M. Hardt , Topological properties of subanalytic sets, to appear in Trans . Amer. Math. Soc. MR 379882 | Zbl 0303.32008 · Zbl 0303.32008 · doi:10.2307/1997218
[27] R.M. Hardt , Triangulation of subanalytic sets and proper light subanalytic maps, preprint . MR 454051 · Zbl 0331.32006