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.