Expansion of α-open sets and decomposition of α-continuous mappings

We introduce the notions of expansion 𝒜 α of α -open sets and 𝒜 α -expansion α -continuous mappings in topological spaces. The main result of this paper is that a map f is α -continuous if and only if it is 𝒜 α -expansion α -continuous and ℬ α -expansion α -continuous, where 𝒜 α , ℬ α are two mutually dual expansions.