It is known that for an $n-$dimensional topological manifold $M$, a foliation is an equivalence relation on $M$. Is there any proof to this? I cannot find any online and would love to see one. It might be trivial but I am a beginner in this subject. Thanks!
2026-03-25 17:51:47.1774461107
Foliations as equivalence relations
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By definition, the leaves of a foliation is a partition of the manifold, and as any partition induces an equivalence relation, so does a foliation. See e.g. Anosov's entry for a foliation in the Encyclopedia of Mathematics: https://encyclopediaofmath.org/index.php?title=Foliation (a "decomposition" is the same as a "partition" in this context).