Brouwer fixed-point theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Brouwer fixed-point theorem" in English language version.

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Milnor 1965, pp. 1–19 Milnor, John W. (1965). Topology from the differentiable viewpoint. Charlottesville: University Press of Virginia. MR 0226651.
Milnor 1978 Milnor, John W. (1978). "Analytic proofs of the 'hairy ball theorem' and the Brouwer fixed-point theorem" (PDF). Amer. Math. Monthly. 85 (7): 521–524. JSTOR 2320860. MR 0505523. Archived (PDF) from the original on 2022-10-09.
Madsen & Tornehave 1997, pp. 39–48 Madsen, Ib; Tornehave, Jørgen (1997). From calculus to cohomology: de Rham cohomology and characteristic classes. Cambridge University Press. ISBN 0-521-58059-5. MR 1454127.
Boothby 1971 Boothby, William M. (1971). "On two classical theorems of algebraic topology". Amer. Math. Monthly. 78 (3): 237–249. doi:10.2307/2317520. JSTOR 2317520. MR 0283792.
Boothby 1986 Boothby, William M. (1986). An introduction to differentiable manifolds and Riemannian geometry. Pure and Applied Mathematics. Vol. 120 (Second ed.). Academic Press. ISBN 0-12-116052-1. MR 0861409.
Dieudonné 1982 Dieudonné, Jean (1982). "8. Les théorèmes de Brouwer". Éléments d'analyse. Cahiers Scientifiques (in French). Vol. IX. Paris: Gauthier-Villars. pp. 44–47. ISBN 2-04-011499-8. MR 0658305.
Kellogg, Li & Yorke 1976. Kellogg, R. Bruce; Li, Tien-Yien; Yorke, James A. (1976). "A constructive proof of the Brouwer fixed point theorem and computational results". SIAM Journal on Numerical Analysis. 13 (4): 473–483. Bibcode:1976SJNA...13..473K. doi:10.1137/0713041. MR 0416010.
Chow, Mallet-Paret & Yorke 1978. Chow, Shui Nee; Mallet-Paret, John; Yorke, James A. (1978). "Finding zeroes of maps: Homotopy methods that are constructive with probability one". Mathematics of Computation. 32 (143): 887–899. doi:10.1090/S0025-5718-1978-0492046-9. MR 0492046.
Hilton & Wylie 1960 Hilton, Peter J.; Wylie, Sean (1960). Homology theory: An introduction to algebraic topology. New York: Cambridge University Press. ISBN 0521094224. MR 0115161.
Nyman, Kathryn L.; Su, Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer.math.monthly.120.04.346, JSTOR 10.4169/amer.math.monthly.120.04.346, MR 3035127

arches.ro

Quotation from Henri Poincaré taken from: P. A. Miquel La catégorie de désordre Archived 2016-03-03 at the Wayback Machine, on the website of l'Association roumaine des chercheurs francophones en sciences humaines

archive.org

Jacques Hadamard: Note sur quelques applications de l'indice de Kronecker in Jules Tannery: Introduction à la théorie des fonctions d'une variable (Volume 2), 2nd edition, A. Hermann & Fils, Paris 1910, pp. 437–477 (French)
Dieudonné, Jean (1989). A History of Algebraic and Differential Topology, 1900–1960. Boston: Birkhäuser. pp. 17–24. ISBN 978-0-8176-3388-2.
Milnor 1965, pp. 1–19 Milnor, John W. (1965). Topology from the differentiable viewpoint. Charlottesville: University Press of Virginia. MR 0226651.

archive.today

This citation comes originally from a television broadcast: Archimède, Arte, 21 septembre 1999

arxiv.org

See F. Brechenmacher L'identité algébrique d'une pratique portée par la discussion sur l'équation à l'aide de laquelle on détermine les inégalités séculaires des planètes CNRS Fédération de Recherche Mathématique du Nord-Pas-de-Calais

auckland.ac.nz

math.auckland.ac.nz

E.g.: S. Greenwood J. Cao Brouwer's Fixed Point Theorem and the Jordan Curve Theorem University of Auckland, New Zealand.

bibmath.net

E.g. F & V Bayart Théorèmes du point fixe on Bibm@th.net Archived December 26, 2008, at the Wayback Machine
V. & F. Bayart Point fixe, et théorèmes du point fixe on Bibmath.net. Archived December 26, 2008, at the Wayback Machine

books.google.com

This version follows directly from the previous one because every convex compact subset of a Euclidean space is homeomorphic to a closed ball of the same dimension as the subset; see Florenzano, Monique (2003). General Equilibrium Analysis: Existence and Optimality Properties of Equilibria. Springer. p. 7. ISBN 9781402075124. Retrieved 2016-03-08.

claremont.edu

scholarship.claremont.edu

Nyman, Kathryn L.; Su, Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer.math.monthly.120.04.346, JSTOR 10.4169/amer.math.monthly.120.04.346, MR 3035127

culture.gouv.fr

Henri Poincaré won the King of Sweden's mathematical competition in 1889 for his work on the related three-body problem: Jacques Tits Célébrations nationales 2004 Site du Ministère Culture et Communication

dml.cz

Kulpa 1989 Kulpa, Władysław (1989). "An integral theorem and its applications to coincidence theorems". Acta Universitatis Carolinae. Mathematica et Physica. 30 (2): 83–90.

doi.org

Brouwer, L. E. J. (1911). "Über Abbildungen von Mannigfaltigkeiten". Mathematische Annalen (in German). 71: 97–115. doi:10.1007/BF01456931. S2CID 177796823.
Freudenthal, Hans (1975). "The cradle of modern topology, according to Brouwer's inedita". Historia Mathematica. 2 (4): 495–502 [p. 495]. doi:10.1016/0315-0860(75)90111-1.
Freudenthal, Hans (1975). "The cradle of modern topology, according to Brouwer's inedita". Historia Mathematica. 2 (4): 495–502 [p. 495]. doi:10.1016/0315-0860(75)90111-1. ... cette dernière propriété, bien que sous des hypothèses plus grossières, ait été démontré par H. Poincaré
Freudenthal, Hans (1975). "The cradle of modern topology, according to Brouwer's inedita". Historia Mathematica. 2 (4): 495–502 [p. 501]. doi:10.1016/0315-0860(75)90111-1.
Schauder, J. (1930). "Der Fixpunktsatz in Funktionsräumen". Studia Mathematica. 2: 171–180. doi:10.4064/sm-2-1-171-180.
Kakutani, S. (1941). "A generalization of Brouwer's Fixed Point Theorem". Duke Mathematical Journal. 8 (3): 457–459. doi:10.1215/S0012-7094-41-00838-4.
For a long explanation, see: Dubucs, J. P. (1988). "L. J. E. Brouwer : Topologie et constructivisme". Revue d'Histoire des Sciences. 41 (2): 133–155. doi:10.3406/rhs.1988.4094.
Boothby 1971 Boothby, William M. (1971). "On two classical theorems of algebraic topology". Amer. Math. Monthly. 78 (3): 237–249. doi:10.2307/2317520. JSTOR 2317520. MR 0283792.
Kellogg, Li & Yorke 1976. Kellogg, R. Bruce; Li, Tien-Yien; Yorke, James A. (1976). "A constructive proof of the Brouwer fixed point theorem and computational results". SIAM Journal on Numerical Analysis. 13 (4): 473–483. Bibcode:1976SJNA...13..473K. doi:10.1137/0713041. MR 0416010.
Chow, Mallet-Paret & Yorke 1978. Chow, Shui Nee; Mallet-Paret, John; Yorke, James A. (1978). "Finding zeroes of maps: Homotopy methods that are constructive with probability one". Mathematics of Computation. 32 (143): 887–899. doi:10.1090/S0025-5718-1978-0492046-9. MR 0492046.
David Gale (1979). "The Game of Hex and Brouwer Fixed-Point Theorem". The American Mathematical Monthly. 86 (10): 818–827. doi:10.2307/2320146. JSTOR 2320146.
Eldon Dyer (1956). "A fixed point theorem". Proceedings of the American Mathematical Society. 7 (4): 662–672. doi:10.1090/S0002-9939-1956-0078693-4.
Nyman, Kathryn L.; Su, Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer.math.monthly.120.04.346, JSTOR 10.4169/amer.math.monthly.120.04.346, MR 3035127

encyclopediaofmath.org

Voitsekhovskii, M.I. (2001) [1994], "Brouwer theorem", Encyclopedia of Mathematics, EMS Press, ISBN 1-4020-0609-8

ghostarchive.org

Teschl, Gerald (2019). "10. The Brouwer mapping degree". Topics in Linear and Nonlinear Functional Analysis (PDF). Graduate Studies in Mathematics. American Mathematical Society. Archived (PDF) from the original on 2022-10-09. Retrieved 1 February 2022.
Milnor 1978 Milnor, John W. (1978). "Analytic proofs of the 'hairy ball theorem' and the Brouwer fixed-point theorem" (PDF). Amer. Math. Monthly. 85 (7): 521–524. JSTOR 2320860. MR 0505523. Archived (PDF) from the original on 2022-10-09.

harvard.edu

ui.adsabs.harvard.edu

Kellogg, Li & Yorke 1976. Kellogg, R. Bruce; Li, Tien-Yien; Yorke, James A. (1976). "A constructive proof of the Brouwer fixed point theorem and computational results". SIAM Journal on Numerical Analysis. 13 (4): 473–483. Bibcode:1976SJNA...13..473K. doi:10.1137/0713041. MR 0416010.

jstor.org

Milnor 1978 Milnor, John W. (1978). "Analytic proofs of the 'hairy ball theorem' and the Brouwer fixed-point theorem" (PDF). Amer. Math. Monthly. 85 (7): 521–524. JSTOR 2320860. MR 0505523. Archived (PDF) from the original on 2022-10-09.
Boothby 1971 Boothby, William M. (1971). "On two classical theorems of algebraic topology". Amer. Math. Monthly. 78 (3): 237–249. doi:10.2307/2317520. JSTOR 2317520. MR 0283792.
David Gale (1979). "The Game of Hex and Brouwer Fixed-Point Theorem". The American Mathematical Monthly. 86 (10): 818–827. doi:10.2307/2320146. JSTOR 2320146.
Nyman, Kathryn L.; Su, Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer.math.monthly.120.04.346, JSTOR 10.4169/amer.math.monthly.120.04.346, MR 3035127

jussieu.fr

ann.jussieu.fr

P. Bich Une extension discontinue du théorème du point fixe de Schauder, et quelques applications en économie Archived June 11, 2011, at the Wayback Machine Institut Henri Poincaré, Paris (2007)

mathdoc.fr

portail.mathdoc.fr

See for example: Émile Picard Sur l'application des méthodes d'approximations successives à l'étude de certaines équations différentielles ordinaires Archived 2011-07-16 at the Wayback Machine Journal de Mathématiques p 217 (1893)

mathnet.ru

mi.mathnet.ru

Myskis, A. D.; Rabinovic, I. M. (1955). "Первое доказательство теоремы о неподвижной точке при непрерывном отображении шара в себя, данное латышским математиком П.Г.Болем" [The first proof of a fixed-point theorem for a continuous mapping of a sphere into itself, given by the Latvian mathematician P. G. Bohl]. Успехи математических наук (in Russian). 10 (3): 188–192.

persee.fr

For a long explanation, see: Dubucs, J. P. (1988). "L. J. E. Brouwer : Topologie et constructivisme". Revue d'Histoire des Sciences. 41 (2): 133–155. doi:10.3406/rhs.1988.4094.

scientiaestudia.org.br

"concerne les propriétés invariantes d'une figure lorsqu'on la déforme de manière continue quelconque, sans déchirure (par exemple, dans le cas de la déformation de la sphère, les propriétés corrélatives des objets tracés sur sa surface". From C. Houzel M. Paty Poincaré, Henri (1854–1912) Archived 2010-10-08 at the Wayback Machine Encyclopædia Universalis Albin Michel, Paris, 1999, p. 696–706

semanticscholar.org

api.semanticscholar.org

Brouwer, L. E. J. (1911). "Über Abbildungen von Mannigfaltigkeiten". Mathematische Annalen (in German). 71: 97–115. doi:10.1007/BF01456931. S2CID 177796823.

st-and.ac.uk

www-groups.dcs.st-and.ac.uk

J. J. O'Connor E. F. Robertson Piers Bohl
J. J. O'Connor E. F. Robertson Luitzen Egbertus Jan Brouwer
J. J. O'Connor E. F. Robertson Luitzen Egbertus Jan Brouwer.

stackexchange.com

math.stackexchange.com

Belk, Jim. "Why is convexity a requirement for Brouwer fixed points?". Math StackExchange. Retrieved 22 May 2015.

tripod.com

jeff560.tripod.com

The term algebraic topology first appeared 1931 under the pen of David van Dantzig: J. Miller Topological algebra on the site Earliest Known Uses of Some of the Words of Mathematics (2007)

ucsc.edu

people.ucsc.edu

Milnor 1978 Milnor, John W. (1978). "Analytic proofs of the 'hairy ball theorem' and the Brouwer fixed-point theorem" (PDF). Amer. Math. Monthly. 85 (7): 521–524. JSTOR 2320860. MR 0505523. Archived (PDF) from the original on 2022-10-09.

ulaval.ca

newton.mat.ulaval.ca

D. Violette Applications du lemme de Sperner pour les triangles Bulletin AMQ, V. XLVI N° 4, (2006) p 17. Archived June 8, 2011, at the Wayback Machine

uni-goettingen.de

resolver.sub.uni-goettingen.de

Brouwer, L. E. J. (1911). "Über Abbildungen von Mannigfaltigkeiten". Mathematische Annalen (in German). 71: 97–115. doi:10.1007/BF01456931. S2CID 177796823.

unice.fr

math1.unice.fr

C. Minazzo K. Rider Théorèmes du Point Fixe et Applications aux Equations Différentielles Archived 2018-04-04 at the Wayback Machine Université de Nice-Sophia Antipolis.

univ-mrs.fr

cmi.univ-mrs.fr

These examples are taken from: F. Boyer Théorèmes de point fixe et applications CMI Université Paul Cézanne (2008–2009) Archived copy at WebCite (August 1, 2010).

universalis.fr

More exactly, according to Encyclopédie Universalis: Il en a démontré l'un des plus beaux théorèmes, le théorème du point fixe, dont les applications et généralisations, de la théorie des jeux aux équations différentielles, se sont révélées fondamentales. Luizen Brouwer by G. Sabbagh

univie.ac.at

mat.univie.ac.at

Teschl, Gerald (2019). "10. The Brouwer mapping degree". Topics in Linear and Nonlinear Functional Analysis (PDF). Graduate Studies in Mathematics. American Mathematical Society. Archived (PDF) from the original on 2022-10-09. Retrieved 1 February 2022.

web.archive.org

E.g. F & V Bayart Théorèmes du point fixe on Bibm@th.net Archived December 26, 2008, at the Wayback Machine
D. Violette Applications du lemme de Sperner pour les triangles Bulletin AMQ, V. XLVI N° 4, (2006) p 17. Archived June 8, 2011, at the Wayback Machine
V. & F. Bayart Point fixe, et théorèmes du point fixe on Bibmath.net. Archived December 26, 2008, at the Wayback Machine
C. Minazzo K. Rider Théorèmes du Point Fixe et Applications aux Equations Différentielles Archived 2018-04-04 at the Wayback Machine Université de Nice-Sophia Antipolis.
Quotation from Henri Poincaré taken from: P. A. Miquel La catégorie de désordre Archived 2016-03-03 at the Wayback Machine, on the website of l'Association roumaine des chercheurs francophones en sciences humaines
"concerne les propriétés invariantes d'une figure lorsqu'on la déforme de manière continue quelconque, sans déchirure (par exemple, dans le cas de la déformation de la sphère, les propriétés corrélatives des objets tracés sur sa surface". From C. Houzel M. Paty Poincaré, Henri (1854–1912) Archived 2010-10-08 at the Wayback Machine Encyclopædia Universalis Albin Michel, Paris, 1999, p. 696–706
See for example: Émile Picard Sur l'application des méthodes d'approximations successives à l'étude de certaines équations différentielles ordinaires Archived 2011-07-16 at the Wayback Machine Journal de Mathématiques p 217 (1893)
P. Bich Une extension discontinue du théorème du point fixe de Schauder, et quelques applications en économie Archived June 11, 2011, at the Wayback Machine Institut Henri Poincaré, Paris (2007)

webcitation.org

These examples are taken from: F. Boyer Théorèmes de point fixe et applications CMI Université Paul Cézanne (2008–2009) Archived copy at WebCite (August 1, 2010).