Multi topological approximations of rough set theory

In this paper, we generalise Pawlak's approximation spaces to topological approximation spaces.These topological approximation spaces are generated using many topological notions such as regular open sets, semi-open sets, pre-open sets, γ-open sets, α-open sets and β-open sets and others.The basic definitions and properties of these topological approximation spaces are introduced and sufficiently illustrated.We put all topological generalisations in one generalisation called m-generalisation spaces.