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

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 iγ , cγ (where γ = σ, π, α, β) introduced by Császár is at the most 25.Explicit expressions for these sets are provided.An example is provided where all the 25 different 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. MSC (2010): primary 54A05; secondary 54A99.