AI 中文总结
本文为带通用导数的o-极小结构构建δ-单元分解框架，关联源单元与有限构型以研究微分拓扑，证明δ-拓扑的抽象曲线选择定理，并给出闭序微分场中抽象曲线芽的渐近代表。
AI 中文摘要
我们为配备通用导数的 o-极小结构构建了单元分解框架。对每个δ-单元，我们关联普通 o-极小类中的源单元与有限构型，使微分拓扑问题可通过有限射影空间研究。随后引入可定义曲线芽的度量空间，将其局部半空间片段与可定义芽的哈代域极大理想的笛卡尔幂等同。利用该芽空间描述，我们证明了δ-拓扑的抽象曲线选择定理。对闭序微分场，我们进一步给出抽象曲线芽的具体渐近代表。
英文摘要
We develop a cell decomposition framework for o-minimal structures equipped with a generic derivation. To a $δ$-cell we associate source cells and finite configurations in ordinary o-minimal sorts, allowing differential-topological questions to be studied through finite jet spaces. We then introduce a metric space of definable curve germs and identify its local half-space pieces with Cartesian powers of the maximal ideal of the Hardy field of definable germs. Using this germ-space description, we prove an abstract curve selection theorem for the $δ$-topology. In the case of closed ordered differential fields, we further describe concrete asymptotic representatives for the abstract curve germs.
Comments41 pages
