A foliation 
of an 
-manifold 
of codimension 
(with 
)
is a partition of 
into disjoint pathwise-connected subsets 
. For the foliation 
of 
,
there must exist 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 Resource. https://mathworld.wolfram.com/Foliation.html