The big fundamental group, big Hawaiian earrings, and the big free groups
type: Item
instance of: scholarly article
title: The big fundamental group, big Hawaiian earrings, and the big free groups
zbMATH Open document ID: 0955.57003
DOI: 10.1016/S0166-8641(99)00104-2
published in: Topology and its Applications
publication date: 2001-02-22T00:00:00Z
review text: In this second of a series of three papers, the `big fundamental group' of a topological space is defined and studied. This big fundamental group is based on maps of big intervals (compact totally ordered connected spaces) rather than the usual unit interval, replacing also homotopy by big homotopy. Then the big Hawaiian earrings are defined as the one-point compactification of an arbitrary number of disjoint open intervals (the classical case corresponding to a countable number of such intervals), and it is shown that the big fundamental group of the big Hawaiian earrings is a big free group in the sense of the paper of the previous review (which is the first of the series; in the third one the fundamental groups of more general one-dimensional spaces will be studied).
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20F34
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 1506030
zbMATH Keywords: big free group
author: James W. Cannon
author: G. Conner
reviewed by: Bruno Zimmermann
MaRDI profile type: Publication
Wikidata QID: Q56444551
description: scientific article; zbMATH DE number 1506030