Let be an -manifold and let denote a partition of into disjoint pathwise-connected subsets. Then is called a foliation of of codimension (with ) if there exists a cover of by open sets , each equipped with a homeomorphism or which throws each nonempty component of onto a parallel translation of the standard hyperplane in . Each is then called a foliation leaf and is not necessarily closed or compact (Rolfsen 1976, p. 284).
Foliation
See also
Confoliation, Cover, Foliation Leaf, Homeomorphism, Manifold, Reeb FoliationExplore with Wolfram|Alpha
References
Candel, A. and Conlon, L. Foliations I. Providence, RI: Amer. Math. Soc., 1999.Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, 1976.Referenced on Wolfram|Alpha
FoliationCite this as:
Weisstein, Eric W. "Foliation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Foliation.html