Taut codimension-one foliations

Assume Countable Choice ${\mathrm{A}\mathrm{C}}_{\omega }$. Let $F$ be a codimension-one regular foliation of a smooth manifold $M$, transversely oriented in this pair. $F$ is taut if for every leaf $L$ of $F$ there is a closed transversal through $L$: an embedded smooth loop $\gamma :S^1\to M$, everywhere transverse to $F$, with $\gamma (S^1)\cap L\mathrm{\ne }\mathrm{\varnothing }$. The empty manifold is taut vacuously, but has no closed transversal. On a nonempty compact connected $M$, the leaf-by-leaf condition is equivalent to the existence of a single closed transversal meeting every leaf, as proved in A taut foliation of a compact connected manifold has a single closed transversal ↗. For a closed oriented three-manifold the sufficient closed-two-form criterion is A leafwise positive closed two-form calibrates a taut foliation ↗; that three-dimensional criterion is not asserted here in other dimensions.