可数群作为紧性的基本群的实现
Realizations of Countable Groups as Fundamental Groups of Compacta
摘要：
是否每一个有限生成群都能被实现为紧度量空间的基本群是一个公开的问题（Pawlikowski）。本文证明了任何可数群都可以实现为四维欧几里得空间的紧致子空间的基本群。根据谢拉定理（另见Pawlikowski），如果群不是非线性生成的，那么这样的空间就不能是局部路径连通的。这种构造补充了Keesling和Rudyak以及Przezdziecki在紧致T2空间中研究的群的实现。
英文摘要：
It is an open question (Pawlikowski) whether every finitely generated group can be realized as a fundamental group of a compact metric space. In this paper we prove that any countable group can be realized as the fundamental group of a compact subspace of four dimensional Euclidean space. According to theorems of Shelah (see also Pawlikowski) such space can not be locally path connected if the group is not finitely generated. This constructions complements realization of groups in the context of compact Hausdorff spaces, that was studied by Keesling and Rudyak, and Przezdziecki .
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