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Locally convex lattices.
Concerning an ideal of the bornographic lattice, we have: THEOREM 1.2.An ideal $H$ of any boundedly closed locally convex lattice $E$ is boundedly closed in the relative topology.An ideal $H$ of any bornographic lattice $E$ is bornographic in the relative topology.PROOF.We shall see the first part.Let $f$ be a linear …