Some transversality theorems

In this paper transversality theorems are proved for canonical transformations, contact transformations, and transformations which preserve volume elements, as well as sections of a fiber bundle whose base and fiber are smooth manifolds. Let $\Omega$ be one of the mapping spaces mentioned, and let $L$ be a smooth submanifold in the space of $r$-jets of the germs of the mappings in $\Omega$. The transversality theorem asserts that a set of mappings in $\Omega$ whose $r$-jet extensions are transversal to $L$ is everywhere dense in $\Omega$.
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