On images of complete topologized subsemilattices in sequential semitopological semilattices
Banakh, Taras, 1968- ; Bardyla, Serhii
A topologized semilattice ▫$X$▫ is called complete if each non-empty chain ▫$C \subset X$▫ has ▫$\inf C \in {\bar{C}}$▫ and ▫$\inf C \in {\bar{C}}$▫. We prove that for any continuous homomorphism ...▫$h: X \rightarrow Y$▫ from a complete topologized semilattice ▫$X$▫ to a sequential Hausdorff semitopological semilattice ▫$Y$▫ the image ▫$h(X)$▫ is closed in ▫$Y$▫.
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