Abstract
L.E.J. Brouwer (1881-1966) had started his career with papers on geometry and mechanics, but by 1909 he had shifted his interests to parts of mathematics far less popular at that time, and in which he was entirely self-taught. He first tackled Hilbert’s famous “5th problem” and showed that all C° groups of transformations of the real line are in fact Lie groups. This work, and attempts to extend it to transformation groups of R2, led him to study what was known at the time about the topology of the plane. This had started with Cantor’s theory of sets, and was closely linked to the general study of functions of real variables and of their often surprising properties; the results that had attracted the most attention were the Jordan theorem on the domains limited by a simple closed curve (1893), and the Peano “curve” filling a square (1890), leading to the investigation of the various meanings that could be given to the word “curve.”
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© 2009 Birkhäuser Boston
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Dieudonné, J. (2009). The Concept of Degree. In: A History of Algebraic and Differential Topology, 1900 - 1960. Modern Birkhäuser Classics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4907-4_7
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DOI: https://doi.org/10.1007/978-0-8176-4907-4_7
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