O-极小结构中的PL与微分拓扑
PL and differential topology in o-minimal structure
摘要：
关于PL，（=分段线性）拓扑的论证在任何序域上的作用方式与在实数域上的作用方式相同，而关于微分拓扑的论证在展开（R，<，0，1，+，cdot）的o-极小结构中的实封闭的域R上的作用方式相同。可定义集最基本的性质之一是R^n中的紧致可定义集可定义同胚于多面体（见[v]）。我们证明了多面体的唯一性PL同胚（O-最小Hauptvermutung）。因此，一个紧致可定义的拓扑流形唯一地具有PL流形结构，并且可以说是驯服的。我们还看到，R上PL和微分拓扑的许多问题都可以转化为实域上的问题。
英文摘要：
Arguments on PL,(=piecewise linear) topology work over any ordered field in the same way as over the real field, and those on differential topology do over a real closed field R in an o-minimal structure that expands (R,<,0,1,+,cdot). One of the most fundamental properties of definable sets is that a compact definable set in R^n is definably homeomorphic to a polyhedron (see [v]). We show uniqueness of the polyhedron up to PL homeomorphisms (o-minimal Hauptvermutung). Hence a compact definable topological manifold admits uniquely a PL manifold structure and is, so to say, tame. We also see that many problems on PL and differential topology over R can be translated to those over the real field.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
