The authors show that a topological group \(G\) is locally pseudocompact iff \(G\) is locally bounded and, for every closed \(G_\delta\)-subgroup \(H\) of \(G\), the quotient space \(G/H\) is locally compact. This result is applied to give a partial positive answer to a problem posed by K. A. Ross in 1965: If \({\mathcal T}_1\) and \({\mathcal T}_2\) are locally pseudocompact group topologies on an Abelian group \(G\) such that \((G,{\mathcal T}_1)\) and \((G,{\mathcal T}_2)\) have the same closed subgroups, then \({\mathcal T}_1\subseteq {\mathcal T}_2\) implies \({\mathcal T}_1 = {\mathcal T}_2\). The same conclusion remains valid for certain non-Abelian groups, for example, if \((G,{\mathcal T}_1)\) is locally compact and \((G,{\mathcal T}_2)\) is locally pseudocompact.
For the entire collection see [Zbl 0903.00047].