Decomposition of Pre-β- Irresolute Maps and g- Closed Sets in Topological Space

Research Paper

Year: 2023 | Month: July | Volume: 10 | Issue: 7 | Pages: 889-901

DOI: https://doi.org/10.52403/ijrr.202307103

Decomposition of Pre-β- Irresolute Maps and g- Closed Sets in Topological Space

AHMED M. RAJAB¹, DHFAR Z. ALI², OHOOD A. HADI³

^1,2,3Department of Mathematics, Faculty of Computer Sciences and Mathematics, University of Kufa, Najaf, Iraq

Corresponding Author: AHMED M. RAJAB

ABSTRACT

This paper explores the decomposition of pre--irresolute (pre--irr) maps and their connection to generalized closed sets (g-closed) in topological space (top. sp.). We provide the necessary background on top. sp., continuity, closed, and related concepts. We introduce the definitions of pre--irr maps and g-closed and discuss their basic properties. The decomposition theorem is presented, stating that every pre--irr map can be decomposed into a composition of a pre--continuous (pre- -cont.) map and a b-irr map. Examples and applications are provided to illustrate the behavior of pre--irr maps and the practical implications of the decomposition theorem. We examine the relationships between pre--cont. maps and pre--irr maps, exploring the conditions under which a pre--irr map is also -irr, and provide a proof for this relationship. The properties of pre--cont. maps, - maps, g- pre--cont. maps, and g--cont. maps are discussed, along with proofs and examples to illustrate their applicability. This paper contributes to the understanding of pre--irr maps, their decomposition, and their relationships with g-closed, providing a foundation for further research in top. sp. and map decompositions.