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

Saharon Shelah

doi:10.1090/S0002-9939-1988-0943095-3

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

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

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.

Original language	English
Pages (from-to)	607-611
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	103
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1988-0943095-3
State	Published - Jun 1988

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10.1090/S0002-9939-1988-0943095-3

Cite this

@article{6b282ae925de4ac6954fffd813037ce5,

title = "Can the fundamental (homotopy) group of a space be the rationals?",

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.",

author = "Saharon Shelah",

year = "1988",

month = jun,

doi = "10.1090/S0002-9939-1988-0943095-3",

language = "אנגלית",

volume = "103",

pages = "607--611",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",