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Hereditarily non-topologizable groups

Gábor Lukács
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Abstract

A group G is non-topologizable if the only Hausdorff group topology that G admits is the discrete one. Is there an infinite group G such that H/N is non-topologizable for every subgroup H <= G and every normal subgroup N <| H? We show that a solution of this essentially group theoretic question provides a solution to the problem of c-compactness.

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Gábor Lukács. 2006-03-21. Hereditarily non-topologizable groups. https://arxiv.org/abs/math/0603513

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