The space of simple closed curves and measured foliation on non-compact orientable surfaces (Q1116125)

A proof is offered for the fact that every open (non-compact) orientable surface (finite or infinite genus) possesses a measured foliation without singularities (in the proof we do not see how \(\alpha\) : [0,1]\(\to M\) could be a proper embedding containing all singular points; probably one has to take an infinite number of such embeddings). Also, the set of isotopy classes of simple closed curves on such a surface is embedded in an infinite-dimensional projective space, in analogy to the case of compact surfaces.