Foliation

Let $M^n$ be an $n$-Manifold and let ${\hbox{\sf F}}=\{F_\alpha\}$ denote a Partition of $M^n$ into Disjoint path-connected Subsets. Then ${\hbox{\sf F}}$ is called a foliation of $M^n$ of codimension $c$ (with $0<c<n$) if there Exists a Cover of $M^n$ by Open Sets $U$, each equipped with a Homeomorphism $h:U\to \Bbb{R}^n$ or $h:U\to \Bbb{R}_+^n$ which throws each nonempty component of $F_\alpha\cap U$ onto a parallel translation of the standard Hyperplane $\Bbb{R}^{n-c}$ in $\Bbb{R}^n$. Each $F_\alpha$ is then called a Leaf and is not necessarily closed or compact.

See also Leaf (Foliation), Reeb Foliation

References

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 284, 1976.