2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78609We prove the consistency (modulo supercompact) of a negative answer to Arhangelskii's problem (some Hausdorff compact space cannot be partitioned to two sets not containing a closed copy of Cantor discontinuum). In this model we have CH. Without CH we get consistency results using a pcf assumption, close relatives of which are necessary for such results.Preliminary ReportLogicGeneral Topologytext