论文标题
在第二类的局部局部O-最低结构中可以确定的函数
Functions definable in definably complete uniformly locally o-minimal structure of the second kind
论文作者
论文摘要
我们研究了第二种密集线性有序的Abelian群（DCULOAS结构）的局部局部O-最低膨胀可定义的连续函数。 我们证明了Arzela-Ascoli定理的变体，用于均匀连续的可定义函数和以下断言：考虑参数化函数$ f：c \ times p \ rightarrow m $，与$ p $相对于$ p $。当$ f $不连续的$ f $不连续的集合的投影图像是尺寸小于$ \ dim p $时，当$ c $关闭和界限时。 此外，我们证明了具有可定义的Tietze扩展特性的Archimedean dculoas结构是O-Wimimal。在附录中，我们表明，当且仅当它拥有可确定的Tietze扩展属性时，订购组的O最低扩展不是半结合的。
We investigate continuous functions definable in a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group (DCULOAS structure). We prove a variant of the Arzela-Ascoli theorem for uniformly continuous definable functions and the following assertion: Consider the parameterized function $f:C \times P \rightarrow M$ which is equi-continuous with respect to $P$. The projection image of the set at which $f$ is discontinuous to the parameter space $P$ is of dimension smaller than $\dim P$ when $C$ is closed and bounded. In addition, we demonstrate that an archimedean DCULOAS structure which enjoys definable Tietze extension property is o-minimal. In the appendix, we show that an o-minimal expansion of an ordered group is not semi-bounded if and only if it enjoys definable Tietze extension property.
