Rough Sets: A Topological View

This paper explores the topological aspects of algebras determined by rough sets. It is well known that the lattice structure of rough sets is characterized by the lattices of the form 2(I) x 3(J). We show that algebras determined by the rough sets are characterized by the condition "any chain of completely prime filters has at most two elements". We introduce the notion of rough topological space in which the basic open set has at most two elements. We further provide representations of rough topological spaces in terms of topologies determined by algebras of rough sets.