On completeness of H-closed pospaces

Abstract

We generalized the characterization of H-closedness for linearly ordered pospaces as follows: A pospace $X$ without an infinite antichain is an H-closed pospace if and only if $X$ is a directed complete and down-complete poset such that sup $L$ and inf $L$ are contained in the closure of $L$ for any nonempty chain $L$ in $X$.