The fundamental groups of certain one-dimensional spaces
type: Item
instance of: scholarly article
title: The fundamental groups of certain one-dimensional spaces
zbMATH Open document ID: 0960.55007
author: Katsuya Eda
published in: Tokyo Journal of Mathematics
publication date: 2001-05-14T00:00:00Z
review text: This paper follows [\textit{K. Eda} and \textit{K. Kawamura}, Topology Appl. 87, No. 3, 163-172 (1998; Zbl 0922.55008)]. The main result is Theorem 1.1 which asserts that under some hypothesis the fundamental group is isomorphic to a subgroup of \(\sigma\)-free product of a family of \(\mathbb{Z}\)'s. It can be regarded as a generalization of van Kampen's theorem. Then some examples are given. They are the Hawaiian earring, the Sierpinski gasket and its three-dimensional analogue, whose fundamental groups are not a free product of nontrivial groups. Theorem 1.4 gives another example. But it could hardly be understood. Maybe that the ``connected groups'' ought to be ``connected components''; and ``accumulation point of \(C\) in \(Y\cup \{\infty\} \cup\{-\infty\}\)'' ought to be ``accumulation point of \(C/ \sim\) in \(Y\cup\{\infty\} \cup \{-\infty\}/ \sim\), where the quotient is to identify each component as a point''. It is regrettable that \S 4 could hardly be understood, too.
reviewed by: Zaisi Zuo
Mathematics Subject Classification ID: 55Q52
Mathematics Subject Classification ID: 55Q07
zbMATH DE Number: 1523376
zbMATH Keywords: Hawaiian earring
zbMATH Keywords: Sierpinski gasket
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1255958814
OpenAlex ID: W2002261108
DOI: 10.3836/TJM/1255958814
description: scientific article; zbMATH DE number 1523376