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A countable
space with an uncountable fundamental group
Jeremy Brazas and Luis Matos
Vol. 12 (2019), No. 3, 381–394
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Abstract |
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Traditional examples of spaces that have an uncountable fundamental group (such as the Hawaiian earring space) are path-connected compact metric spaces with uncountably many points. We construct a compact, path-connected, locally path-connected topological space with countably many points but with an uncountable fundamental group. The construction of , which we call the “coarse Hawaiian earring” is based on the construction of the usual Hawaiian earring space where each circle is replaced with a copy of the four-point “finite circle”. |
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Keywords
fundamental group, countable topological space, finite
topological space, Hawaiian earring, coarse Hawaiian
earring
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Mathematical Subject Classification 2010
Primary: 54D10, 55Q52
Secondary: 57M05, 57M10
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Milestones
Received: 8 April 2017
Revised: 12 June 2018
Accepted: 9 September 2018
Published: 14 December 2018
Communicated by Józef H. Przytycki
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Authors |
| Jeremy Brazas | |
| Department of Mathematics West Chester University West Chester, PA United States |
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| Luis Matos | |
| School of Mathematics Georgia Institute of Technology Atlanta, GA United States |
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