Generalized αii-Closed Sets in Ordinary Topological Spaces

Abstract

The primary objective of this research is to introduce a novel type of generalized sets, which we have termed generalized αii-closed and generalized αii-open sets. The properties of these sets and their relationships with other types of sets have been rigorously investigated through a series of mathematical proofs, including, if  is such that  is a generalized closed set in , then  is generalized closed set in relation to ), if  are generalized closed sets, then so is their intersection, each generalized closed(open) set is a generalized closed(open) set, each generalized closed(open) set is a generalized closed(open) set, each semi-generalized closed(open) set is a generalized closed(open) set, a set in, is generalized open set when and if only if where is closed set within, if, wherein, is a generalized open set, then so is, and finally, If are generalized open sets, then so is their union.

Keywords

• i-open sets
• ii-open sets
• ii-continuity
• generalized αii-closed sets
• generalized αii-open sets