On H-closed topological semigroups and semilattices - Chuchman, I.; Gutik, O. (Algebra and Discrete Mathematics, 2007)
In this paper, we show that if S is an H-closed
topological semigroup and e is an idempotent of S, then eSe is
an H-closed topological semigroup. We give sufficient conditions
on a linearly ordered topological semilattice to be H-closed. Also
we prove that any H-closed locally compact topological semilattice
and any H-closed topological weakly U-semilattice contain minimal idempotents. An example of a countably compact topological
semilattice whose topological space is H-closed is constructed.