We introduce a new notion called weakly contra-m-continuous functions as functions from a set satisfying some minimal conditions into a topological space. We obtain some characterizations and several properties of such functions. The functions enable us to formulate a unified theory of several modifications of weak contra-continuity due to Baker .
A new kind of sets called generalized w-closed (briefly gw-closed) sets is introduced and studied in a topological space by using the concept of weak structures introduced by Á. Császár in . The class of all gw-closed sets is strictly larger than the class of all w-closed sets. Furthermore, g-closed sets (in the sense of N. Levine ) is a special type of gw-closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of w-regular and w-normal spaces have been given.
Summary New classes of sets called O-closed sets and Os-closed sets are introduced and studied. Also, we introduce and study O-continuous functions and Os-continuous functions and prove pasting lemma for these functions. Moreover, we introduce classes of topological spaces O-T1/2 and O-Ts.
We introduce a new notion called contra-(μ,λ)-continuous functions as functions on generalized topological spaces . We obtain some characterizations and several properties of such functions. The functions enable us to formulate a unified theory of several modifications of contra-continuity due to Dontchev .