On convergence of nets in Riesz space

Banach lattices can be equipped with many convergence structures such as order, relative regular, unbounded order, unbounded norm convergence, and absolutely un bounded weak convergence. While some of these convergences are topological, some of them are not. However they are convergences that only preserve the order struc ture. Unbounded order convergence was firstly defined by De Marr under the name of "individual convergence" and then examined under the name of "uo-convergence" by Nakano. Recently, many researchers have focused on the properties of different types of unbounded convergence. Unbounded norm convergence was firstly introduced and studied by Troitsky. Finally, Zabeti uaw-convergence defined and worked on. In this thesis, all these types of convergence is studied and the relationships between them are investigated.