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

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.

arXiv comment5 pages; minor changes in the introduction and references

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