The fundamental groups of one-dimensional wild spaces and the Hawaiian earring

Katsuya Eda

doi:10.1090/S0002-9939-01-06431-0

The fundamental groups of one-dimensional wild spaces and the Hawaiian earring

Katsuya Eda

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

8 Citations (Scopus)

Abstract

Let X be a one-dimensional space which contains a copy C of a circle and let it not be semi-locally simply connected at any point on C. Then the fundamental group of X cannot be embeddable into a free σ-product of n-slender groups, for instance, the fundamental group of the Hawaiian earring. Consequently, any one of the fundamental groups of the Sierpinski gasket, the Sierpinski curve, and the Menger curve is not embeddable into the fundamental group of the Hawaiian earring.

Original language	English
Pages (from-to)	1515-1522
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	130
Issue number	5
DOIs	https://doi.org/10.1090/S0002-9939-01-06431-0
Publication status	Published - 2002

Keywords

Fundamental group
Hawaiian earring
Menger curve
One-dimensional
Sierpinski gasket

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0002-9939-01-06431-0

Fingerprint Dive into the research topics of 'The fundamental groups of one-dimensional wild spaces and the Hawaiian earring'. Together they form a unique fingerprint.

Cite this

@article{8fbf0ff9daa945ca828dbacfac19bf4c,

title = "The fundamental groups of one-dimensional wild spaces and the Hawaiian earring",

abstract = "Let X be a one-dimensional space which contains a copy C of a circle and let it not be semi-locally simply connected at any point on C. Then the fundamental group of X cannot be embeddable into a free σ-product of n-slender groups, for instance, the fundamental group of the Hawaiian earring. Consequently, any one of the fundamental groups of the Sierpinski gasket, the Sierpinski curve, and the Menger curve is not embeddable into the fundamental group of the Hawaiian earring.",

keywords = "Fundamental group, Hawaiian earring, Menger curve, One-dimensional, Sierpinski gasket",

author = "Katsuya Eda",

year = "2002",

doi = "10.1090/S0002-9939-01-06431-0",

language = "English",

volume = "130",

pages = "1515--1522",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "5",

}

TY - JOUR

T1 - The fundamental groups of one-dimensional wild spaces and the Hawaiian earring

AU - Eda, Katsuya

PY - 2002

Y1 - 2002

N2 - Let X be a one-dimensional space which contains a copy C of a circle and let it not be semi-locally simply connected at any point on C. Then the fundamental group of X cannot be embeddable into a free σ-product of n-slender groups, for instance, the fundamental group of the Hawaiian earring. Consequently, any one of the fundamental groups of the Sierpinski gasket, the Sierpinski curve, and the Menger curve is not embeddable into the fundamental group of the Hawaiian earring.

AB - Let X be a one-dimensional space which contains a copy C of a circle and let it not be semi-locally simply connected at any point on C. Then the fundamental group of X cannot be embeddable into a free σ-product of n-slender groups, for instance, the fundamental group of the Hawaiian earring. Consequently, any one of the fundamental groups of the Sierpinski gasket, the Sierpinski curve, and the Menger curve is not embeddable into the fundamental group of the Hawaiian earring.

KW - Fundamental group

KW - Hawaiian earring

KW - Menger curve

KW - One-dimensional

KW - Sierpinski gasket

UR - http://www.scopus.com/inward/record.url?scp=0035994116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035994116&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-01-06431-0

DO - 10.1090/S0002-9939-01-06431-0

M3 - Article

AN - SCOPUS:0035994116

VL - 130

SP - 1515

EP - 1522

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -