On strongly α-I-Open sets and a new mapping

Abstract

In this paper, we introduce the notion of strongly α-I-open sets in ideal topological spaces and investigate some of their properties. Further we study the continuous functions for the above set and derive the some of their properties. RESUMENEn este trabajo, se introduce la noción del gran conjunto α-I-abierto ideal en espacios topológicos y se investigan algunas de sus propiedades. Además se estudian las funciones continuas para el conjunto y parte de sus propiedades.

Note on \(F^\star\)-spaces

“…An ideal topological space (X, τ, I) is called I g -Alexandroff space [7] if any intersection of open sets in (X, τ, I) is I g -open. A subset A of an ideal topological space (X, τ, I) is said to be R-I-open set [8] (resp., α-I-open set [3], t-I-set [9], α -I-set [9], pre-I-open [10], B I -set [9], C I -set [9], b-I-open [9], strongly α-I-open set [11], strongly pre-I-open set [12], strongly b-I-open set [13] The following lemmas will be useful in the sequel.…”