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 ( H -closed topological semilattice) under which L contains a maximal (minimal) element. We also give sufficient conditions for a linearly ordered topological partially ordered space to be H -closed. We prove that a linearly ordered H -closed topological semilattice is an H -closed topological pospace and show that in general, this is not true. We construct an example of an H -closed topological pospace with a non- H -closed maximal chain and give sufficient conditions under which a maximal chain of an H -closed topological pospace is an H -closed topological pospace.