Closure Operators and Lattice Extensions

摘要

For closure operators Γ and Δ on the same set Χ, we say that Δ is a weak (resp. strong) extension of Γ if Cl(Χ, Γ) is a complete meet-subsemilattice (resp. complete sublattice) of Cl(Χ, Δ). This context is used to describe the extensions of a finite lattice that preserve various properties.