On δb-open continuous functions

In this paper, we define an almost δb-continuity, which is a weaker form of R-map and we investigate and obtain its some properties and characterizations. Finally, we show that a function f: (X, τ) → (Y, φ) is almost δb-continuous if and only if f: (X, τs) → (Y, φs) is b-continuous, where τs and φs are semiregularizations of τ and φ, respectively.