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Cantor–Schoenflies Topology

In: L.E.J. Brouwer – Topologist, Intuitionist, Philosopher

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  • Dirk van Dalen

    (Utrecht University, Department of Philosophy)

Abstract

When Brouwer continued his investigations into Hilbert 5, he discovered that his main topology source, Schoenflies Bericht, was far from correct. He set himself to straighten out the defective parts; the best known fall out of this research was his work on indecomposable continua, with the spectacular example of three domains with one common boundary. The chapter also contains the story of Brouwer’s research on fixed points on the sphere and his translation theorem (on fixed point free continuous maps of the plane onto itself). He simultaneously produced a number of papers on vector field on surfaces. The best known result was the hairy ball theorem: a continuous vector field on a sphere must be zero or infinite at at least one point.

Suggested Citation

  • Dirk van Dalen, 2013. "Cantor–Schoenflies Topology," Springer Books, in: L.E.J. Brouwer – Topologist, Intuitionist, Philosopher, edition 127, chapter 0, pages 119-148, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4471-4616-2_4
    DOI: 10.1007/978-1-4471-4616-2_4
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