论文标题
度量空间的分解
A factorization of metric spaces
论文作者
论文摘要
我们首先证明，对于每个可元空间$ x $，对于每个封闭的子集$ f $，其补充为零维，可以将$ x $的空间嵌入封闭子集$ f $的产品空间和可作为封闭子集的封闭子集$ f $的产品空间中。使用该定理，我们接下来显示了指标和超特质的延伸器的存在，它们保留了指标的特性，例如完整性，符合性，超特质，其分形维度和大规模结构。该结果包含作者的某些扩展定理的超法定理。
We first prove that for every metrizable space $X$, for every closed subset $F$ whose complement is zero-dimensional, the space $X$ can be embedded into a product space of the closed subset $F$ and a metrizable zero-dimensional space as a closed subset. Using this theorem, we next show the existence of extensors of metrics and ultrametrics, which preserve properties of metrics such as the completeness, the properness, being an ultrametrics, its fractal dimensions, and large scale structures. This result contains some of the author's extension theorems of ultrametrics.
