Contra-open functions and contra-closed functions. (English) Zbl 0903.54008

Summary: Generalization of open functions and closed functions, which are called contra-open and contra-closed, respectively, are introduced. Contra-open functions are characterized by having closed images of open sets whereas contra-closed functions have open images of closed sets. Relationships between these functions and weak forms of opennesss and closedness are investigated. Additional properties of contra-open functions and contra-closed functions are established. In particular, conditions are established under which a contra-open function has a closed graph.


54C10 Special maps on topological spaces (open, closed, perfect, etc.)