A note on some generalized closure and interior operators in a topological space

Abstract

If X is a topological space and A X, then the number of distinct sets that can be obtained from A by using all possible compositions for operators i , c (where = ; ; ; ) introduced by Cs asz ar is at the most 25. Explicit expressions for these sets are provided. An example is provided where all the 25 di erent sets are determined. The result is also discussed for special cases such as when the space is extremally disconnected, resolvable, open-unresolvable, and partition spaces.