On images of complete topologized subsemilattices in sequential semitopological semilattices
Taras Banakh, Serhii Bardyla

TL;DR
The paper proves that the image of a complete topologized semilattice under a continuous homomorphism into a sequential Hausdorff semitopological semilattice is always closed.
Contribution
It establishes a new closure property for images of complete topologized semilattices under continuous homomorphisms in sequential settings.
Findings
Images are closed under continuous homomorphisms
Completeness ensures closure in sequential semitopological semilattices
Advances understanding of topological semilattice homomorphisms
Abstract
A topologized semilattice is called complete if each non-empty chain has and . We prove that for any continuous homomorphism from a complete topologized semilattice to a sequential Hausdorff semitopological semilattice the image is closed in .
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