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Brouwer, L. E. J. --- 51 BROUWER, LUITZEN EGBERTUS JAN --- Mathematics--BROUWER, LUITZEN EGBERTUS JAN --- 51 BROUWER, LUITZEN EGBERTUS JAN Mathematics--BROUWER, LUITZEN EGBERTUS JAN --- 515.12 --- 515.12 General topology --- General topology --- Mathematicians --- Brouwer, Luitzen Egbertus Jan, --- Mathématiciens --- Biography --- Biographies --- Brouwer, L.E.J. (Luitzen Egbertus Jan) --- Netherlands --- Brouwer, Luitzen Egbertus Jan --- Mathematicians - Netherlands - Biography. --- Histoire des mathematiques --- Biographie --- 20e siecle

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Based on Sperner's lemma the fixed point theorem of Brouwer is proved. Rather than presenting also other beautiful proofs of Brouwer's fixed point theorem, many nice applications are given in some detail. Also Schauder's fixed point theorem is presented which can be viewed as a natural generalization of Brouwer's fixed point theorem to an infinite-dimensional setting. Finally, Tarski's fixed point theorem is applied to differential equations in Banach spaces.

Banachräume --- Brouwer --- SchauderFixed points --- Fixpunkt --- Anwendungen --- Banach spaces --- verification methods

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Cet ouvrage s'appuie sur les ressources de la logique dialogique pour proposer une lecture originale de l'intuitionnisme mathématique, assumant sa composante subjectiviste. L'enrichissement du dispositif des dialogues au moyen d'outils sémiotiques permet aussi de renouveler le concept de dialogue.

Mathématiques intuitionnistes. --- Brouwer, Luitzen Egbertus Jan, 1881-1966 --- Mathématiques intuitionnistes --- Mathématiques --- Dialogue (littérature) --- Brouwer, Luitzen Egbertus Jan, --- Critique et interprétation. --- Intuitionistic mathematics --- Mathematics --- Brouwer, L. E. J. (Luitzen Egbertus Jan), 1881-1966

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Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics.   Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

Brouwer, Luitzen Egbertus Jan --- Brouwer, L. E. J. (Luitzen Egbertus Jan), 1881-1966. --- Intuitionistic mathematics. --- Mathematicians -- Netherlands -- Biography. --- Mathematics -- Philosophy. --- Mathematicians --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Brouwer, L. E. J. --- Brouwer, Luitzen Egbertus Jan, --- Mathematics. --- History. --- Mathematical logic. --- Topology. --- Popular works. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Popular Science, general. --- Logic, Symbolic and mathematical. --- Science (General). --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Algebras, Linear --- Annals --- Auxiliary sciences of history --- Math --- Science --- Mathematicians. --- Symbolisk logik. --- Brouwer, Luitzen E. J., --- Netherlands. --- Brouwer, Bertus,

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Peinture hollandaise --- Van ostade (isack) --- Brouwer (adriaen) --- Hals (frans), peintre hollandais, 1581?-1666 --- Van ostade (adriaen) --- Catalogues --- 17e siecle