One-dimensional foliations on topological manifolds

Abstract

Let X be an (n+1)-dimensional manifold, Δ be a one-dimensional foliation on X, and p: X → X / Δ be a quotient map.We will say that a leaf ω of Δ is special whenever the space of leaves X / Δ is not Hausdorff at ω.We present necessary and sufficient conditions for the map p: X → X / Δ to be a locally trivial fibration under assumptions that all leaves of Δ are non-compact and the family of all special leaves of Δ is locally finite.

Keywords

• шарування
• некомпактна поверхня
• розшарування
• селекція