Topology Proceedings 33 (2009), pp. 269-275

Hereditarily non-topologizable groups

Gábor Lukács

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 \vartriangleleft H? We show that an answer to this essentially group theoretic question provides a solution to the problem of c-compactness.

Keywords: non-topologizable, c-compact, topological group, hereditarily non-topologizable, totally minimal, small invariant neighborhoods, torsion group

Mathematics Subject Classification: 20F05, 22C05(22A05, 54H11)

Document formats: PDF file 144.3 Kb

Topology Proceedings, Volume 33 (2009)
Subscription information