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The number of non-solutions to an equation in a group and non-topologizable torsion-free groups

Anton A. Klyachko·Anton V. Trofimov
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Abstract

It is shown that, for any pair of cardinals with infinite sum, there exist a group and an equation over this group such that the first cardinal is the number of solutions to this equation and the second cardinal is the number of non-solutions to this equation. A countable torsion-free non-topologizable group is constructed.

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Anton A. Klyachko, Anton V. Trofimov. 2004-11-10. The number of non-solutions to an equation in a group and non-topologizable torsion-free groups. https://doi.org/10.1515/jgth.2005.8.6.747

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