有理数上的自由拓扑群

General Topology and its Applications Pub Date : 1979-02-01 DOI:10.1016/0016-660X(79)90027-8

Temple H. Fay, Edward T. Ordman, Barbara V. Smith Thomas

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引用次数: 28

摘要

本文研究了有理数上的Graev自由拓扑群的拓扑结构。我们证明了这个自由群不是k空间，并且不能携带由其长度小于或等于n的词的子空间所产生的弱拓扑。作为本研究的工具，我们建立了自由群中净收敛的一些性质，以及与自由群拓扑结构密切相关的某些正则映射的一些性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The free topological group over the rationals

In this paper we investigate the topological structure of the Graev free topological group over the rationals. We show that this free group fails to be a k-space and fails to carry the weak topology generated by its subspaces of words of length less than or equal to n. As tools in this investigation we establish some properties of net convergence in free groups and also some properties of certain canonical maps which are closely related to the topological structure of free groups.

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