ABSTRACT

This note provides a short, self-contained proof of the famous fact that any countable metric space without isolated points is homeomorphic to the space of rational numbers. The discussion is carried out entirely in the language of metric spaces.

中文翻译：

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没有孤立点的可数度量空间

摘要

该注释提供了一个简短的独立证据，证明了一个著名的事实，即没有孤立点的任何可数度量空间都是有理数空间的同胚。讨论完全以度量空间的语言进行。