Locally modular lattices and locally distributive lattices

Maeda, Shûichirô

doi:10.1090/S0002-9939-1974-0340132-4

Locally modular lattices and locally distributive lattices
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Proc. Amer. Math. Soc. 44 (1974), 237-243 Request permission

Abstract:

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 ${T_1}$-topologies of an infinite set is locally distributive.

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