Codimension one foliation and the prime spectrum of a ring

Let F be a transversally oriented co dimension -one foliation of class C (R), r > 0, on a closed manifold M. A leaf class of a leaf F is the union of all leaves having the same closure as F. Let X be the leaf classes space and X-0 be the union of all open subsets of X homeomorphic to R or S1. In [3, Theorem 3.15] it is shown that if a codimension one foliation has a finite height, then the singular part of the space of leaf classes is homeomorphic to the prime spectrum (or simply the spectrum) of unitary commutative ring. In this paper we prove that the singular part of the space of leaf classes is homeomorphic to the spectrum of unitary commutative ring if and only if every family of totaly ordered leaves is bounded below.