超三维空间与剪枝树支系空间同构

arXiv - MATH - General Topology Pub Date : 2024-07-31 DOI:arxiv-2407.21763

Itamar Bellaïche

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引用次数: 0

摘要

本文证明了每一个超对称空间都与一棵修剪过的树的树冠空间（即树冠的子空间）同构。此外，本文还通过超对称空间代表树的特征，描述了超对称空间的几个拓扑性质。这种方法表明，应该通过研究自然有序的修剪树来研究超三叉空间的拓扑性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Ultrametrizable spaces are homeomorphic to clade spaces of pruned trees

This paper demonstrates that every ultrametric space is homeomorphic to a clade space of a pruned tree, i.e., a subspace of a tree's canopy. Furthermore, it characterizes several topological properties of ultrametrizable spaces through the features of their representing trees. This approach suggests that topological properties of ultrametrizable spaces should be studies via the study of naturally ordered pruned trees.

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arXiv - MATH - General Topology

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