A general theory of self-similarity II: recognition
A general theory of self-similarity II: recognition
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自相似的一般理论II：识别
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
T. Leinster
中科院分区：
文献类型：
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作者：
T. Leinster
本文涉及 math.DS/0411344 中定义的拓扑空间的自相似性。我展示了如何识别自相似空间，或更准确地说，自相似系统的通用解决方案。示例包括标准单纯形（通过重心细分实现自相似）和迭代函数系统的解。也许令人惊讶的是，每个紧凑的可度量空间至少在一种方面是自相似的。由此得出关于康托集在紧凑的可度量空间中的作用的经典结果。
This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the standard simplices (self-similar by barycentric subdivision) and solutions of iterated function systems. Perhaps surprisingly, every compact metrizable space is self-similar in at least one way. From this follow the classical results on the role of the Cantor set among compact metrizable spaces.