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EVERY COUNTABLE GROUP IS THE FUNDAMENTAL GROUP OF SOME COMPACT SUBSPACE OF $\mathbb{R}^{4}$
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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.
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- © 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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