Suppose that there is a locally integrable foliation on a manifold $M$ such that any of its leaves is not dense in $M$. Does that mean that we can factorize $M$ by this distribution and get a topological space with at least one non-trivial continuous function on it?
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$\begingroup$ You can always define the space of leaves of any foliation. What specific properties do you want on the space of leaves ? Do you want it to be separated, to be a manifold,... $\endgroup$– Tsemo AristideCommented Aug 13, 2016 at 20:28
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