Let X be a connected non-compact 2-dimensional manifold possibly with boundary and <$EDELTA> be a foliation on X such that each leaf <$Eomega~symbol <174>~DELTA> is homeomorphic to <$Eroman bold R> and has a trivially foliated neighborhood. Such foliations on the plane were studied by W. Kaplan who also gave their topological classification. He proved that the plane splits into a family of open strips foliated by parallel lines and glued along some boundary intervals. However W. Kaplanіs construction depends on a choice of those intervals, and a foliation is described in a non-unique way. We propose a canonical cutting by open strips which gives a uniqueness of classifying invariant. We also describe topological types of closures of those strips under additional assumptions on <$EDELTA>.

• Максименко Сергій Іванович (1974–) (фізико-математичні науки)

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