## On a type of generalized open sets.(English)Zbl 1236.54019

Summary: A new class of sets called $$\mu$$-generalized closed (briefly $$\mu g$$-closed) sets in generalized topological spaces is introduced and studied. The class of all $$\mu g$$-closed sets is strictly larger than the class of all $$\mu$$-closed sets (in the sense of Á. Császár). Furthermore, $$g$$-closed sets (in the sense of N. Levine) are a special type of $$\mu g$$-closed sets in a topological space. Some of their properties are investigated here.
Finally, some characterizations of $$\mu$$-regular and $$\mu$$-normal spaces are given.

### MSC:

 54D10 Lower separation axioms ($$T_0$$–$$T_3$$, etc.) 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54C08 Weak and generalized continuity 54C10 Special maps on topological spaces (open, closed, perfect, etc.)