Change of topologies and rough sets

In this book, we use three types of expansion of topologies. The first, is simple expansion of topologies which is a method used in constructing finer topology from a given topology via a non open subset. The concept of simple expansion of topology was first introduced by Levine(1964). Although a similar concept had been discussed by Hewit (1943). The second type of expansions of topologies is the local discrete expansion of topologies using any subset, which was introduced by Young(1971). Finally, in the last twenty years, contributions for generalization of topologies have been appeared in many papers .The concept of a supratopologies was introduced by Mashhour et-al.(1983). Also, Abd EL-Monsef, et-al.(1987) have been introduced the concept of simple expansion of supratopologies and the concept of local discrete expansion of supratopologies. This work aims to solve some problems in rough set theory using changes of topologies. For example, some undefinable sets with respect to the original topologies can become definable in view of some of its expansion.