On (γ∗,β∗γ∗,β∗)-almost-pre-continuous mappings in topological spaces

In this paper, we introduced the notion of γ∗γ∗-regular-open sets and γ∗γ∗-δδ.open sets and studied some of their basic properties and investigated the relationship between them. Also we introduced the notion of γ∗γ∗-δδ-TiTii=0,12,1,2 spaces and characterized them using γ∗γ∗-δδ.open sets and γ∗γ∗-δδ.closed sets. Finally the concepts of (γ∗,β∗γ∗,β∗)-almost-pre-continuous mappings and (γ∗,β∗γ∗,β∗)-almost-pre-open (closed) mappings and studied some of their basic properties.