hα-Open Sets in Topological Spaces | ||
| Journal of Education and Science | ||
| Article 7, Volume 31, Issue 3, September 2022, Pages 91-98 PDF (837.96 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/edusj.2022.134241.1251 | ||
| Authors | ||
| Baedaa S. Abdullah1; Sabih W. Askandar* 2; Ruqayah N. Balo3 | ||
| 1Mathematics Department/college of education for pure sciences/mosul university | ||
| 2Mathematics/College of Education for Pure Science/Mosul University | ||
| 3mathematics department/college of education for pure sciences/mosul university | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| h∝-open set,,; ,،,؛h∝-continuous mapping,,; ,،,؛h∝-open mapping,,; ,،,؛h∝-totally continuous mapping,,; ,،,؛h∝-irresolute mapping | ||
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