Codimension One Foliation and the Prime Spectrum of a Ring
Keywords:space of leaf classes., prime spectrum, Compact foliations
Let F be a transversally oriented codimension-one foliation of class Cr, 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 X0 be the union of all open subsets of X homeomorphic to R or S1. In [2, 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.
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