On images of complete topologized subsemilattices in sequential semitopological semilattices
Abstract
A topologized semilattice X is called complete if each non-empty chain C⊂ X has ∈f C∈ C and C∈ C. We prove that for any continuous homomorphism h:X 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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