On Chains in H-Closed Topological Pospaces

We study chains in an H-closed topological partially ordered space. We give sufficient conditions for a maximal chain L in an H-closed topological partially ordered space such that L contains a maximal (minimal) element. Also we give sufficient conditions for a linearly ordered topological partially ordered space to be H-closed. We prove that any H-closed topological semilattice contains a zero. We show that a linearly ordered H-closed topological semilattice is an H-closed topological pospace and show that in the general case this is not true. We construct an example an H-closed topological pospace with a non-H-closed maximal chain and give sufficient conditions that a maximal chain of an H-closed topological pospace is an H-closed topological pospace.