: Matemáticas: hairy ball theorem

topology > algebraic topology > hairy ball theorem

topology > differential topology > hairy ball theorem

hairy ball theorem

The hairy ball theorem of algebraic topology (sometimes called the hedgehog theorem in Europe) states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in R³ to every point p on a sphere such that f(p) is always tangent to the sphere at p, then there is at least one pole, a point where the field vanishes (a p such that f(p) = 0).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hairy_ball_theorem)

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