在o-极小结构中曲线上连续的函数
Functions continuous on curves in o-minimal structures
摘要：
本文给出了o-极小域上的非振荡曲线的充要条件，使得对任何有界可定义函数，该函数在曲线的初始段上的芽可连续扩张到闭可定义集.这种情况被转化为一个关于类型的问题：对于任何有界可定义函数，有一个可定义集合，该集合包含函数在其上连续的类型，并且可以连续扩展到集合的闭包，对于$n$类型有什么条件？所有这些类型都是可定义的，我们给出了精确的条件，相当于存在一个所需的可定义集。
英文摘要：
We give necessary and sufficient conditions on a non-oscillatory curve in an o-minimal field such that, for any bounded definable function, the germ of the function on an initial segment of the curve can be continuously extended to a closed definable set. This situation is translated into a question about types: What are the conditions on an $n$-type such that, for any bounded definable function, there is a definable set containing the type on which the function is continuous, and can be extended continuously to the set's closure? All such types are definable, and we give the precise conditions that are equivalent to existence of a desired definable set.
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。
