论文标题
同时扩展高功率的指标和超计量
Simultaneous extensions of metrics and ultrametrics of high power
论文作者
论文摘要
在本文中，广义指标是指在一般线性有序的阿贝尔群体中采用值的指标。使用Hahn场，我们首先证明，对于每个通用的度量空间，如果该公制范围组的Archimedean等效类别的集合具有无限的降低序列，则该空间的每个非空封闭子集都是环境空间的均匀缩回。接下来，我们同时构建广义指标和超特质的扩展。从广义指标的延伸器的存在来看，我们使用广义指标的完整性来表征通用衡量空间的最终紧凑性。
In this paper, generalized metrics mean metrics taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every generalized metric space, if the set of the Archimedean equivalence classes of the range group of the metric has an infinite decreasing sequence, then every non-empty closed subset of the space is a uniform retract of the ambient space. Next we construct simultaneous extensions of generalized metrics and ultrametrics. From the existence of extensors of generalized metrics, we characterize the final compactness of generalized metrizable spaces using the completeness of generalized metrics.
