Let F be a foliation of codimension 2 on a compact manifold with at least one
non-compact leaf. We show that then F must contain uncountably many non-compact
leaves. We prove the same statement for oriented p-dimensional foliations of
arbitrary codimension if there exists a closed p form which evaluates
positively on every compact leaf. For foliations of codimension 1 on compact
manifolds it is known that the union of all non-compact leaves is an open set
[A Haefliger, Varietes feuilletes, Ann. Scuola Norm. Sup. Pisa 16 (1962)
367-397].Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-12.abs.htm