Foliation

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).

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.