Hereditarily non-topologizable groups

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.

v0.99, 4 pages

References in corpus (3)

• Reflection principle characterizing groups in which unconditionally closed sets are algebraic
• The number of non-solutions to an equation in a group and non-topologizable torsion-free groups
• Hereditarily h-complete groups

Cited by in corpus (3)

• On topologizable and non-topologizable groups
• Arnautov's problems on semitopological isomorphisms
• Hereditarily minimal topological groups