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EVERY COUNTABLE GROUP IS THE FUNDAMENTAL GROUP OF SOME COMPACT SUBSPACE OF
$\mathbb{R}^{4}$
Part of:
Homotopy groups
Published online by Cambridge University Press: 17 April 2015
Abstract
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For every countable group $G$ we construct a compact path connected subspace
$K$ of
$\mathbb{R}^{4}$ such that
${\it\pi}_{1}(K)\cong G$. Our construction is much simpler than the one found recently by Virk.
Keywords
MSC classification
- Type
- Research Article
- Information
- Copyright
- © 2015 Australian Mathematical Publishing Association Inc.
References
Pawlikowski, J., ‘The fundamental group of a compact metric space’, Proc. Amer. Math. Soc. 126 (1998), 3083–3087.CrossRefGoogle Scholar
Virk, Ž., ‘Realizations of countable groups as fundamental groups of compacta’, Mediterr. J. Math. 10 (2013), 1573–1589.CrossRefGoogle Scholar
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