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

Abstract

We introduce the notions of expansion 𝒜α of α-open sets and 𝒜α-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 𝒜α-expansion α-continuous and ℬα-expansion α-continuous, where 𝒜α, ℬα are two mutually dual expansions.