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分离的网的差异与排位等效的差异
Michael Dymond1, Vojtěch Kaluža2
1School of Mathematics, University of Birmingham, Watson Building, Edgbaston, Birmingham, B15 2TT UK.
概括
我们为分离的网络引入了等价关系的等级体系,根据位移大小对它们进行分类. 这个框架从有边界的到不分辨的等价值范围,提供了在欧几里德空间中比较点集的新方法.
科学领域:
- 几何测量理论 几何测量理论
- 集合理论 集合理论
- 拓学的拓学
背景情况:
- 分离的网在几何分析中是基本的.
- 现有的等价关系,如边界位移和 Bilipschitz 等价关系有局限性.
- 需要对分离的网进行更细致的分类.
研究的目的:
- 引入欧几里德空间中分离网的等价关系的新层次结构.
- 定义 - - 位移等价值被凸增长函数所索引.
- 探索这些等价值的光谱和它们的区别.
主要方法:
- 基于对比映射和位移边界的-位移等价性的定义.
- 分析从有界位移到不谨慎等价的频谱.
- 与现有的等价关系进行比较,包括 bilipschitz 等价.
主要成果:
- 建立了分离网的-位移等值的等级体系.
- 证明了这些等价值对不同类别的异常类别的是不同的.
- 展示了-位移等价值和 Bilipschitz等价值之间的关系.
结论:
- 拟议的层次结构为分离网络的分类提供了一个精细的框架.
- - 位移等效为几何分析提供了一个灵活的工具.
- 这项工作弥合了现有的概念,并引入了对净等价值的新视角.
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