On images of complete topologized subsemilattices in sequential semitopological semilattices

Abstract

A topologized semilattice $X$ is called complete if each non-empty chain $C\subset X$ has $\inf C\in \bar{C}$ and $\sup C\in \bar{C}$. We prove that for any continuous homomorphism $h:X\to Y$ from a complete topologized semilattice $X$ to a sequential Hausdorff semitopological semilattice $Y$ the image $h(X)$ is closed in $Y$.

6 pages

References in corpus (6)

• Characterizing chain-compact and chain-finite topological semilattices
• On linearly ordered $H$-closed topological semilattices
• Completeness and absolute $H$-closedness of topological semilattices
• The closedness of complete subsemilattices in functionally Hausdorff semitopological semilattices
• Complete topologized posets and semilattices
• The interplay between weak topologies on topological semilattices

Cited by in corpus (3)

• The closedness of complete subsemilattices in functionally Hausdorff semitopological semilattices
• Characterizing categorically closed commutative semigroups
• The Lawson number of a semitopological semilattice