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Proceedings of the American Mathematical Society

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Can the fundamental (homotopy) group of a space be the rationals?


Author: Saharon Shelah
Journal: Proc. Amer. Math. Soc. 103 (1988), 627-632
MSC: Primary 55Q05; Secondary 03E15, 03E40
DOI: https://doi.org/10.1090/S0002-9939-1988-0943095-3
MathSciNet review: 943095
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Abstract: We prove that for any topological space which is metric, compact (hence separable) path connected and locally path connected, its homotopy group is not the additive group of the rational, moreover if it is not finitely generated then it has the cardinality of the continuum.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0943095-3
Article copyright: © Copyright 1988 American Mathematical Society

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