On linearly ordered $H$-closed topological semilattices
  We 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. 
Oleg Gutik and Du\v{s}an Repov\v{s}