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2019 A countable space with an uncountable fundamental group
Jeremy Brazas, Luis Matos
Involve 12(3): 381-394 (2019). DOI: 10.2140/involve.2019.12.381

Abstract

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 T 0 compact, path-connected, locally path-connected topological space H with countably many points but with an uncountable fundamental group. The construction of H , which we call the “coarse Hawaiian earring” is based on the construction of the usual Hawaiian earring space = n 1 C n where each circle C n is replaced with a copy of the four-point “finite circle”.

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Jeremy Brazas. Luis Matos. "A countable space with an uncountable fundamental group." Involve 12 (3) 381 - 394, 2019. https://doi.org/10.2140/involve.2019.12.381

Information

Received: 8 April 2017; Revised: 12 June 2018; Accepted: 9 September 2018; Published: 2019
First available in Project Euclid: 5 February 2019

zbMATH: 07033137
MathSciNet: MR3905336
Digital Object Identifier: 10.2140/involve.2019.12.381

Subjects:
Primary: 54D10, 55Q52
Secondary: 57M05, 57M10

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 3 • 2019
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