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• W2078110899 abstract "Various embedding problems of lattices into complete lattices are solved. We prove that for any join-semilattice S with the minimal join-cover refinement property, the ideal lattice Id S of S is both algebraic and dually algebraic. Furthermore, if there are no infinite D-sequences in J(S), then Id S can be embedded into a direct product of finite lower bounded lattices. We also find a system of infinitary identities that characterize sublattices of complete, lower continuous, and join-semidistributive lattices. These conditions are satisfied by any (not necessarily finitely generated) lower bounded lattice and by any locally finite, join-semidistributive lattice. Furthermore, they imply M. Erné’s dual staircase distributivity. On the other hand, we prove that the subspace lattice of any infinite-dimensional vector space cannot be embedded into any ℵ0-complete, ℵ0-upper continuous, and ℵ0-lower continuous lattice. A similar result holds for the lattice of all order-convex subsets of any infinite chain." @default.
• W2078110899 created "2016-06-24" @default.
• W2078110899 creator A5073101686 @default.
• W2078110899 date "2005-08-01" @default.
• W2078110899 modified "2023-10-12" @default.
• W2078110899 title "Sublattices of complete lattices with continuity conditions" @default.
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• W2078110899 doi "https://doi.org/10.1007/s00012-005-1878-4" @default.
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