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

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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.
5 pages; minor changes in the introduction and references

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Group Theory, General Topology, 20F05, 20F06, 22A05, 54H11

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http://salesiana.dossiersoluciones.com/handle/123456789/97060

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411156
 http://arxiv.org/abs/math/0411156
 Journal of Group Theory, Volume: 8 (2005), Issue: 6 Pages: 747-754 (under the title "The number of non-solutions of an equation in a group")
 doi:10.1515/jgth.2005.8.6.747

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