On the first homology of Peano continua

被引：2

作者：

Conner, Gregory R. ^{[1
]}

Corson, Samuel M. ^{[2
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

来源：

FUNDAMENTA MATHEMATICAE | 2016年 / 232卷 / 01期

关键词：

fundamental group; homology; descriptive set theory; SPACE;

D O I：

10.4064/fm232-1-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer a proof of the clarification.

引用

页码：41 / 48

页数：8

共 7 条

[1] Bell J.L., 2005, Boolean-valued models and independence proofs, V3rd
[2] On the fundamental groups of one-dimensional spaces
Cannon, J. W.
Conner, G. R.
[J]. TOPOLOGY AND ITS APPLICATIONS, 2006, 153 (14) : 2648 - 2672
[3] Fremlin D.H., 1984, CONSEQUENCES MARTINS
[4] Moschovakis YN, 2009, Descriptive Set Theory. Mathematical surveys and monographs
[5] Mycielski J., 1964, Fund. Math, V55, P139, DOI [10.4064/fm-55-2-139-147, DOI 10.4064/FM-55-2-139-147]
[6] The fundamental group of a compact metric space
Pawlikowski, J
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (10) : 3083 - 3087
[7] CAN THE FUNDAMENTAL (HOMOTOPY) GROUP OF A SPACE BE THE RATIONALS
SHELAH, S
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 103 (02) : 627 - 632

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