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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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: http://dx.doi.org/10.1090/S0002-9939-1988-0943095-3
PII: S 0002-9939(1988)0943095-3
Article copyright: © Copyright 1988 American Mathematical Society