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This paper aims to construct foliations F that are stable, meaning that any other foliation close to F is conjugate to F by a diffeomorphism. Our main result yields examples of stable Riemannian foliations F with dense leaves. To our knowledge, these are the first examples of stable Riemannian foliations that are not Hausdorff.
Stephane Geudens (Tue,) studied this question.