High Quality Content by WIKIPEDIA articles! In mathematics, Reeb sphere theorem, named after Georges Reeb, states that A closed oriented connected manifold M n that admits a singular foliation having only centers is homeomorphic to the sphere Sn and the foliation has exactly two singularities. A singularity of a foliation F is of Morse type if in its small neighborhood all leaves of the foliation are levels of a Morse function, being the singularity a critical point of the function. The singularity is a center if it is a local extremum of the function; otherwise, the singularity is a saddle.

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