## hairy ball

(topology) A result in topology stating that a continuous vector field on a sphere is always zero somewhere. The name comes from the fact that you can't flatten all the hair on a hairy ball, like a tennis ball, there will always be a tuft somewhere (where the tangential projection of the hair is zero). An immediate corollary to this theorem is that for any continuous map f of the sphere into itself there is a point x such that f(x)=x or f(x) is the antipode of x. Another corollary is that at any moment somewhere on the Earth there is no wind.

Last updated: 2002-01-07

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