Closure operators and lattice extensions (Q1765959)

Let \(\Gamma \) be a closure operator on a set \(X\). Then Cl\((X,\Gamma )\) denotes the lattice of \(\Gamma \)-closed subsets of \(X\). If \(\Gamma \) and \(\Delta \) are closure operators on the same set \(X\), then \(\Delta \) is a weak (resp. strong) extension of \(\Gamma \) if Cl\((X,\Gamma )\) is a complete meet-subsemilattice (resp. complete sublattice) of Cl\((X,\Delta )\). The paper deals with such extensions on finite lattices.