The fundamental groups of one-dimensional spaces and spatial homomorphisms
type: Item
instance of: scholarly article
title: The fundamental groups of one-dimensional spaces and spatial homomorphisms
zbMATH Open document ID: 1032.55013
DOI: 10.1016/S0166-8641(01)00214-0
author: Katsuya Eda
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: The author proves that, for one-dimensional Peano continua which are locally complicated at every point (not semi-locally simply connected at any point), the homeomorphism type is determined by the fundamental group. That is, the actual points of such a space are encoded in its fundamental group: points are captured in equivalence classes of the Hawaiian earring subgroups of the fundamental group.
Mathematics Subject Classification ID: 55Q20
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 55Q70
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 20F34
Mathematics Subject Classification ID: 55Q52
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54F50
zbMATH DE Number: 1879069
zbMATH Keywords: fundamental grup
zbMATH Keywords: Hawaiian earring
zbMATH Keywords: Peano continuum
zbMATH Keywords: fundamental group
zbMATH Keywords: one-dimensional spaces
zbMATH Keywords: spatial homomorphism
reviewed by: James W. Cannon
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1879069