On chains in $H$-closed topological pospaces

Details On chains in $H$-closed topological pospaces On chains in $H$-closed topological pospaces

2008-04-09

arxiv.org/abs/0804.1449v2

Order 27:1 (2010), 69-81.

Mathematics

General Topology

We have rewritten and substantially expanded the manuscript

Scientific paper

10.1007/s11083-010-9140-x

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.

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