Preorder characterizations of lower separation axioms and their applications to foliations and flows
Abstract
In this paper, we characterize several lower separation axioms C0, CD, CR, CN, λ-space, nested, SYS, SYY, SYS, and Sδ using pre-order. To analyze topological properties of (resp. dynamical systems) foliations, we introduce notions of topology (resp. dynamical systems) for foliations. Then proper (resp. compact, minimal, recurrent) foliations are characterized by separation axioms. Conversely, lower separation axioms are interpreted into the condition for foliations and several relations of them are described. Moreover, we introduce some notions for topologies from dynamical systems and foliation theory.
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