On different modes of order convergence and some applications

We give a thorough overview of the different notions for order convergence that are found in literature and provide systematic comparison associated topologies. As an application this study we prove result related to topology on von Neumann algebras, complementing started Chetcuti et al. (Stud. Math. 230:95-120, 2015). show every atomic algebra (not necessarily \(\sigma \)-finite) restriction bounded parts M coincides with \)-strong \(s(M,M_*)\). recall methods 2015) rest heavily assumption \)-finiteness. Furthermore, semi-finite measure space, complete picture relations between topologies \(L^\infty \) duality \(\langle L^1, L^\infty \rangle its topology.