The function ${\epsilon }_X$ assigns to each point of a given continuum X the closure of the family of all continua that contain x in their interior. We define the class $S(\epsilon )$ of continua for which the function ${\epsilon }_X$ is continuous. On the other hand, we consider some natural diagram involving the function ${\epsilon }_X$ and commutativity of this diagram defines a class of mappings $M(\epsilon )$. We investigate classes $S(\epsilon )$ and $M(\epsilon )$, and relations between them.

中文翻译：

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函数 epsilon 定义的映射和空间

功能 ${\epsilon }_X$为给定的连续体X的每个点分配内部包含x的所有连续体的族的闭包。我们定义类$秒(\epsilon )$ 连续体的函数 ${\epsilon }_X$是连续的。另一方面，我们考虑一些涉及函数的自然图${\epsilon }_X$ 该图的可交换性定义了一类映射 $米(\epsilon )$. 我们调查班级$秒(\epsilon )$ 和 $米(\epsilon )$，以及它们之间的关系。