The fundamental groups of one-dimensional spaces

Katsuya Eda; Kazuhiro Kawamura

The fundamental groups of one-dimensional spaces

Katsuya Eda, Kazuhiro Kawamura

Research output: Contribution to journal › Article › peer-review

Abstract

Let X be a space of dimension at most 1. Then, the fundamental group is isomorphic to a subgroup of the first Čech homotopy group based on finite open covers. Consequently, for a one-dimensional continuum X, the fundamental group is isomorphic to a subgroup of the first Čech homotopy group.

Original language	English
Pages (from-to)	163-172
Number of pages	10
Journal	Topology and its Applications
Volume	87
Issue number	3
Publication status	Published - 1998

Keywords

First Čech homotopy group
Fundamental group
One-dimensional

ASJC Scopus subject areas

Geometry and Topology

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title = "The fundamental groups of one-dimensional spaces",

abstract = "Let X be a space of dimension at most 1. Then, the fundamental group is isomorphic to a subgroup of the first {\v C}ech homotopy group based on finite open covers. Consequently, for a one-dimensional continuum X, the fundamental group is isomorphic to a subgroup of the first {\v C}ech homotopy group.",

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AB - Let X be a space of dimension at most 1. Then, the fundamental group is isomorphic to a subgroup of the first Čech homotopy group based on finite open covers. Consequently, for a one-dimensional continuum X, the fundamental group is isomorphic to a subgroup of the first Čech homotopy group.

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KW - One-dimensional

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