Locally modular lattices and locally distributive lattices
Shûichirô Maeda · Proceedings of the American Mathematical Society · 1974
A locally modular (resp. locally distributive) lattice is a lattice with a congruence relation and each of whose equivalence class has sufficiently many elements and is a modular (resp. distributive) sublattice. Both the lattice of all closed subspaces of a locally convex space and the lattice of projections of a locally finite von Neumann algebra are locally modular. The lattice of all T 1 {T_1} -topologies of an infinite set is locally distributive.