G**β-Continuous and G**β-Irresolute Mappings in Topological Spaces

Topology being somehow very recent in nature but has got tremendous applications over almost all other fields. Theoretical or fundamental topology is a bit dry but the application part is what drives crazy once we get used. Topology has applications in various fields of Science and Technology, like applications to Biology, Robotics, GIS, Engineering, Computer Sciences. Topology though being a part of mathematics but it has influenced the whole world with so strong effects and incredible applications. The concept of continuity is fundamental in large parts of contemporary mathematics. In the nineteenth century, precise definitions of continuity were formulated for functions of a real or complex variable, enabling mathematicians to produce rigorous proofs of fundamental theorems of real and complex analysis, such as the Intermediate Value Theorem, Taylor’s Theorem, the Fundamental Theorem of Calculus, and Cauchy’s Theorem. In the early years of the Twentieth Century, the concept of continuity was generalized so as to be applicable to functions between metric spaces, and subsequently to functions between topological spaces. Topology is an area of mathematics concerned with the properties of space that are preserved under continuous deformations including stretching and bending but not tearing. In 2023, Dr. T. Delcia and M. S, Thillai introduced a new type of closed sets called g**β-closed sets and investigated their basic properties including their relationship with already existing concepts in Topological Spaces. In this paper, we introduce g**β-continuous function, g**β-irresolute function, g**β-open function, g**β-closed function, pre-g**β-open function, and pre-g**β-closed function, and investigate properties and characterizations of these new types of mappings in topological spaces.