Preorder characterizations of lower separation axioms and their applications to foliations and flows

Tomoo Yokoyama

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arXiv · 1708.06626

Preorder characterizations of lower separation axioms and their applications to foliations and flows

Tomoo Yokoyama

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Abstract

In this paper, we characterize several lower separation axioms $C_0, C_D$, $C_R$, $C_N$, $\lambda$-space, nested, $S_{YS}$, $S_{YY}$, $S_{YS}$, and $S_{\delta}$ 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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Tomoo Yokoyama. 2017-08-20. Preorder characterizations of lower separation axioms and their applications to foliations and flows. https://arxiv.org/abs/1708.06626

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