Generalized Contra-Continuous Mappings in Binary Topological Spaces

Abstract

The study of generalized forms of continuity has played an important role in the development of modern topology. In recent years, several extensions of classical topological concepts have been introduced in order to investigate more complex mapping structures. One of the important generalizations of continuity is contra-continuity, in which the inverse image of every open set is closed. On the other hand, binary topological spaces provide a generalized framework where ordered pairs of subsets are used to define open and closed structures. We present a new classes class of generalized contra-continuous mappings, known as generalized continuous contour maps, in binary topological spaces topologies in this paper, and we examine explore thei fundamental basic properties. Several connections between binary contra-continuous continuous mappings are discovered, and generalized binary closed sets are created. establishments. On the interrelation of inclusion, the composition of mappings, and the characteristics of mapping and preservation, numerous structural findings pertaining to inclusion relations are found. characteristics. Given examples and counterexamples, non-examples, to demonstrate the independent autonomy of the newly defined concepts. conditions. The findings of this study have broadened the scope of the current theory of generalized topology and established a more comprehensive framework for analyzing mappings in the context of binary topological structures. mapping out the topology. In addition to binary topology and general continuity, these findings could also be helpful for future studies on topology and its potential applications in nonlinear mathematical models.