2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174695We give a criterium when a linearly ordered topological semilattice is $H$-closed. We also prove that any linearly ordered $H$-closed topological semilattice is absolutely $H$-closed and we show that every linearly ordered semilattice is a dense subsemilattice of an $H$-closed topological semilattice.Group TheoryGeneral Topology06A12; 06F30; 22A15; 22A26; 54H12text