非局部连通空间 I：度量空间上的覆盖与分支覆盖
Non-locally connected spaces I: Coverings and branched coverings on metric spaces
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中文总结 AI 辅助
研究一般度量空间上覆盖与分支覆盖，通过提升连续统发展理论及替代同伦理论，推广经典结果，并研究其在球面分支覆盖动力学中的应用及意义。
中文摘要 AI 辅助
我们给出了一般（非局部连通）度量空间上覆盖与分支覆盖的定义，并研究它们的提升性质。该理论通过提升连续统而非曲线来发展。描绘了一种替代同伦理论，并给出了推广经典结果的版本。我们研究了其在球面分支覆盖动力学中的应用，并提供了几个例子来说明所得结果的意义。
英文摘要
Whether a rational function can have an indecomposable continuum as its Julia set is a fundamental open problem in complex dynamics. We settle this negatively for one of the most classical examples of an indecomposable continuum: we prove that the Knaster continuum cannot be the Julia set of any rational function. To obtain this result, we develop a theory of coverings and branched coverings on general (non-locally connected) metric spaces. We introduce a new Euler characteristic and extend the Riemann--Hurwitz formula to a wider class of spaces, including continua for which the classical shape-theoretic invariants are trivial.
