度量空间中整环的素端
Prime ends for domains in metric spaces
摘要：
本文在相当一般的假设下，给出了度量空间中整环的质端的一个新定义。我们将我们的主要目标与Carathéodory和Näkki的目标进行比较。利用曲线族的\p -模定义了模端点和素端点，并讨论了它们与素端点的关系。我们提供了单例素数结束的特征，并将它们与边界点的可达性的概念，并介绍了一个拓扑上的素数结束边界。我们还研究了素端边界和Mazurkiewicz边界之间的关系。推广了John整环的概念，引入了几乎John整环，并研究了在John整环、几乎John整环和边界连通的整环上的素端.
英文摘要：
In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Carathéodory and Näkki. Modulus ends and prime ends, defined by means of the \p-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.
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