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

共 25 条

[1] Addison J.W., 1959, Fundam. Math., V46, P337
[2] [Anonymous], 1951, T MAT I STEKLOVA 2, DOI DOI 10.1090/TRANS2/029/02
[3] [Anonymous], 1970, Ann. Math. Logic, DOI [10.1016/0003-4843(70)90009-4, DOI 10.1016/0003-4843(70)90009-4]
[4] BELL J, 1985, DESIGN, P9
[5] On fundamental groups with the quotient topology
Brazas, Jeremy
Fabel, Paul
[J]. JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, 2015, 10 (01) : 71 - 91
[6] EQUIVALENCES GENERATED BY FAMILIES OF BOREL SETS
BURGESS, JP
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 69 (02) : 323 - 326
[7] Calcut JS, 2009, TOPOL P, V34, P339
[8] On the fundamental groups of one-dimensional spaces
Cannon, J. W.
Conner, G. R.
[J]. TOPOLOGY AND ITS APPLICATIONS, 2006, 153 (14) : 2648 - 2672
[9] A NOTE ON AUTOMATIC CONTINUITY
Conner, Gregory R.
Corson, Samuel M.
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 147 (03) : 1255 - 1268
[10] On the first homology of Peano continua
Conner, Gregory R.
Corson, Samuel M.
[J]. FUNDAMENTA MATHEMATICAE, 2016, 232 (01) : 41 - 48

← 1 2 3 →