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Generalized αii-Closed Sets in Ordinary Topological Spaces | ||
| Journal of Education and Science | ||
| Article 8, Volume 34, Issue 1, January 2025, Pages 67-74 PDF (670.74 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/edusj.2024.154840.1515 | ||
| Authors | ||
| Muna Y Abbas* ; Sabih W. Askandar | ||
| Department of Mathematics, College of Education for Pure Science, University of Mosul, Mosul, Iraq | ||
| 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 | ||
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