2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67693We revisit the known problem whether each compact topology is contained in a maximal compact topology and collect some partial answers to this question. For instance we show that each compact topology is contained in a compact topology in which convergent sequences have unique limits. We also answer a question of D.E. Cameron by showing that each sequentially compact topology is contained in a maximal sequentially compact topology. We finally observe that each sober compact T_1-topology is contained in a maximal compact topology and that each sober compact T_1-topology which is locally compact or sequential is the infimum of a family of maximal compact topologies.General Topology54A10; 54B15; 54D10; 54D30; 54G20text