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- W1604920584 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a one-dimensional space which contains a copy <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C> <mml:semantics> <mml:mi>C</mml:mi> <mml:annotation encoding=application/x-tex>C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of a circle and let it not be semi-locally simply connected at any point on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C period> <mml:semantics> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>C.</mml:annotation> </mml:semantics> </mml:math> </inline-formula> Then the fundamental group of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> cannot be embeddable into a free <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sigma> <mml:semantics> <mml:mi>σ<!-- σ --></mml:mi> <mml:annotation encoding=application/x-tex>sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-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." @default.
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- W1604920584 date "2001-11-09" @default.
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- W1604920584 title "The fundamental groups of one-dimensional wild spaces and the Hawaiian earring" @default.
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