hα-Open Sets in Topological Spaces

• Published in: al-Tarbiyah wa-al-ʻilm lil-ʻulūm al-insānīyah : majallah ʻilmīyah muḥakkamah taṣduru ʻan Kullīyat al-Tarbiyah lil-ʻUlūm al-Insānīyah fī Jāmiʻat al-Mawṣil Vol. 31; no. 3; pp. 91 - 98
• Main Authors: Baedaa Abdullah, Sabih Askandar, Ruqayah Balo
• Format: Journal Article
• Language: Arabic
• Published: College of Education for Pure Sciences 01-09-2022
• Subjects: h∝-continuous mapping; h∝-irresolute mapping; h∝-open mapping; h∝-open set; h∝-totally continuous mapping
• ISSN: 1812-125X; 2664-2530
• DOI: 10.33899/edusj.2022.134241.1251

In our work we introduced a new type of open sets is defined as follows: If for each set that is not empty M in X, M≠X and M ∈τ^∝such that A ⊆ int(A∪M). then A in (X,τ) is named h∝-open set. We also go through the relationship between h∝- open sets and a variety of other open set types as h-open sets, open sets, semi-open sets and ∝-open sets. We proved that each h-open and open set is h∝-open and there is no relationship between∝-open sets and semi-open sets with h∝-open sets. Furthermore, we begin by introducing the concepts of h∝-continuous mappings, h∝-open mappings, h∝-irresolute mappings, and h∝-totally continuous mappings, We proved that each h-continuous mapping in any topological space is h∝-continuous mapping, each continuous mapping in any topological space is h∝-continuous mapping and there is no relationship between∝-continuous mappings and semi-continuous mappings with h∝-continuous mappings as well as some of its features. Finally, we look at some of the new class's separation axioms.