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
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U2 - 10.1090/S0002-9939-01-06431-0
DO - 10.1090/S0002-9939-01-06431-0
M3 - Article
AN - SCOPUS:0035994116
SN - 0002-9939
VL - 130
SP - 1515
EP - 1522
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 5
ER -