On Generalized δ- Pre-Closed Set in Topological Spaces

Abstract

In his 1970 [1] work, Levine introduced generalized closed sets (g-closed), from which the notion of generalized open sets (g-open) follows by defining them as the complements of generalized closed sets. This study presents and examines a newly defined class of sets, denoted by generalized Pre–closed sets (g P- closed). It builds upon our earlier research on generalized semi - closed sets (gs - closed) [2] by extending the underlying framework and introducing a different generalized class. The paper establishes several essential properties of the proposed sets, including their behavior with respect to intersections, unions, and set inclusion, and investigates their connections with related generalized topological concepts. To demonstrate the validity of the theoretical results, a collection of illustrative examples together with counterexamples is provided.