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## Typical Properties of Leaves of Cartan Foliations with Ehresmann Connection

Journal of Mathematical Sciences. 2016. Vol. 219. No. 1. P. 112-124.

We consider a Cartan foliation (M,F) of an arbitrary codimension q admitting an
Ehresmann connection such that all leaves of (M,F) are embedded submanifolds of M.
We prove that for any foliation (M,F) there exists an open, not necessarily connected,
saturated, and everywhere dense subset M0 of M and a manifold L0 such that the induced
foliation (M0, FM0) is formed by the fibers of a locally trivial fibration with the standard
fiber L0 over (possibly, non-Hausdorff) smooth q-dimensional manifold. In the case of
codimension 1, the induced foliation on each connected component of the manifold M0 is
formed by the fibers of a locally trivial fibration over a circle or over a line.