Let T be a foliation on a two-manifold M. Denote the topology closure of each leaf L of F by L{top}-. A sequence of proper inclusions (L{sub}1){top}- {is contained in} (L{sub}2){top}-{is contained in} ... {is contained in} (L{sub}k){top}-, where each L{sub}i is a recurrent leaf of F, is called a nest of length k. The maximal length of various nests is known as the depth of the foliations F. It is well known that if F is orientable and M is compact, the depth of F is at most one. In this paper, we show that on any orientable, compact two-manifold, there exist nonorientable foliations of infinite depth. This work negatively answers the Aranson conjecture [1].
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