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Homomorphisms into the Fundamental Group of One-Dimensional and Planar Peano ContinuaKent, Curtis Andrew 07 July 2008 (has links) (PDF)
Let X be a planar or one-dimensional Peano continuum. Let E be a Hawaiian Earring with fundamental group H. We show that every homomorphism from H to the fundamental group of X is conjugate to a homomorphism which is induced by a continuous function.
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Pro-Covering Fibrations of the Hawaiian EarringCallor, Nickolas Brenten 01 December 2014 (has links) (PDF)
Let H be the Hawaiian Earring, and let H denote its fundamental group. Assume (Bi) is an inverse system of bouquets of circles whose inverse limit is H. We give an explicit bijection between finite normal covering spaces of H and finite normal covering spaces of Bi. This bijection induces a correspondence between a certain family of inverse sequences of these covering spaces. The correspondence preserves the inverse limit of these sequences, thus offering two methods of constructing the same limit. Finally, we characterize all spaces that can be obtained in this fashion as a particular type of fibrations of H.
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Regular Fibrations over the Hawaiian EarringMcGinnis, Stewart Mason 01 April 2019 (has links)
We present a family of fibrations over the Hawaiian earring that are inverse limits of regular covering spaces over the Hawaiian earring. These fibrations satisfy unique path lifting, and as such serve as a good extension of covering space theory in the case of nonsemi-locally simply connected spaces. We give a condition for when these fibrations are path-connected.
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