On linearly ordered $H$-closed topological semilattices

TL;DR

This paper establishes criteria for $H$-closedness in linearly ordered topological semilattices, proves their absolute $H$-closedness, and shows their dense embedding into $H$-closed semilattices.

Contribution

It provides new criteria for $H$-closedness, proves absolute $H$-closedness for these structures, and demonstrates their dense embedding into $H$-closed semilattices.

Findings

Criteria for $H$-closedness in linearly ordered topological semilattices

Any $H$-closed linearly ordered semilattice is absolutely $H$-closed

Every linearly ordered semilattice densely embeds into an $H$-closed semilattice

Abstract

We give a criterium when a linearly ordered topological semilattice is $H$-closed. We also prove that any linearly ordered $H$-closed topological semilattice is absolutely $H$-closed and we show that every linearly ordered semilattice is a dense subsemilattice of an $H$-closed topological semilattice.