On definable subgroups of the fundamental group

被引：2

作者：

Corson, Samuel M. ^{[1
]}

机构：

[1] Univ Basque Country, Ikerbasque Basque Fdn Sci & Matemat Saila, Sarriena S-N, E-48940 Leioa, Bizkaia, Spain

来源：

TOPOLOGY AND ITS APPLICATIONS | 2019年 / 258卷

关键词：

Fundamental group; Metric spaces; Descriptive set theory;

D O I：

10.1016/j.topol.2019.03.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present several new theorems concerning the first fundamental group of a path connected metric space. Among the results proven are strengthenings of the main theorems of [23] and [7]. A compactness theorem for the fundamental group of a Peano continuum is given. We also show that a free decomposition of the fundamental group of a locally path connected Polish space cannot be nonconstructive. Numerous other results and examples illustrating the sharpness of our theorems are provided. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：336 / 357

页数：22

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