自相似空间中自相似粗粒化的存在性
On the Existence of a Self-Similar Coarse Graining of a Self-Similar Space
摘要：
证明了同胚于自相似空间的拓扑空间是自相似的。存在一个自相似空间$S$，它的粗粒度与$S$同胚.因此，$S$的粗粒化又是自相似的。同样地，$S$的自相似粗粒化的粗粒化也是自相似的。这些情况无休止地成功。这种自相似的$S$实际上是从一个强烈的二次动力学产生的。
英文摘要：
A topological space homeomorphic to a self-similar space is demonstrated to be self-similar. There exists a self-similar space $S$ whose coarse graining is homeomorphic to $S$. The coarse graining of $S$ is, therefore, self-similar again. In the same way, the coarse graining of the self-similar coarse graining of $S$ is, furthermore, self-similar. These situations succeed endlessly. Such a self-similar $S$ is generated actually from an intense quadratic dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
