Some types of contra-preclosed functions in topological spaces

This thesis introduces and studies new kinds of class functions contra functions defined in topological spaces, namely contra-preclosed functions related by some generalization of closed sets from topological space which are preclosed with preopen sets in topological space. It also investigates a new generalization of some kinds of contra-precontinuous function. Bi-contra-precontinuous functions are presented. It has four goals: First, we'll recollect several generalizations for open and closed sets in topological space, such as preopen, preclosed, semi-open, and g-closed sets, along with their attributes and operations. We'll also recall certain topological space preclosed functions. The second purpose provided weak and strong contra-preclosed functions in topological space, together with their attributes and linkages. Third, demonstrate the composition of certain classes of contra preclosed functions in topological space and establish associated theorems. All grantee criteria are met. Limit these examined functions, please. The fourth aim presented several forms of contra precontinuous functions in topological space and gave the essential conditions for proving their key theorems. It also explored some types of Bi-contra continuous functions in topological space.