Group topologies making every continuous homomorphic image to a compact group connected (Q2125129)

In this paper, the author proves that if an abelian group \(G\) can be equipped with a group topology making all of its continuous homomorphic images to a compact group connected, then it admits a MinAP (minimally almost periodic) group topology, hence for every positive natural number \(m\) the subgroup \(mG\) of \(G\) is either the trivial group or has infinite cardinality by a result of \textit{D. Dikranjan} and \textit{D. Shakhmatov} [``Final solution of Protasov-Comfort's problem on minimally almost periodic group topologies'', Preprint, \url{arXiv:1410.3313}].