Gromov- Hausdorff空间中的度量树

IF 0.2 Q4 MATHEMATICS

Commentationes Mathematicae Universitatis Carolinae Pub Date : 2023-11-13 DOI:10.14712/1213-7243.2023.012

Yoshito Ishiki

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引用次数: 0

摘要

利用度量空间的楔形和，对所有紧致可度量空间，构造紧致可度量空间的拓扑嵌入到限定值有限的Gromov—Hausdorff空间中所有度量树的集合中。作为它的应用，我们证明了所有度量树的集合是路径连通的，并且它的所有非空开子集具有无限的拓扑维数。

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Metric trees in the Gromov--Hausdorff space

Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As its application, we show that the set of all metric trees is path-connected and all its nonempty open subsets have infinite topological dimension.

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来源期刊

Commentationes Mathematicae Universitatis Carolinae MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量