hα-Open Sets in Topological Spaces
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 set...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Arabic |
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College of Education for Pure Sciences
2022-09-01
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| Series: | مجلة التربية والعلم |
| Subjects: | |
| Online Access: | https://edusj.mosuljournals.com/article_174956_f40d28d40eb2b9d6731dba30a0e35796.pdf |
| _version_ | 1811214299008335872 |
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| author | Baedaa Abdullah Sabih Askandar Ruqayah Balo |
| author_facet | Baedaa Abdullah Sabih Askandar Ruqayah Balo |
| author_sort | Baedaa Abdullah |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T06:00:56Z |
| format | Article |
| id | doaj.art-dd5792095f78461bbb633f895316e3e2 |
| institution | Directory Open Access Journal |
| issn | 1812-125X 2664-2530 |
| language | Arabic |
| last_indexed | 2024-04-12T06:00:56Z |
| publishDate | 2022-09-01 |
| publisher | College of Education for Pure Sciences |
| record_format | Article |
| series | مجلة التربية والعلم |
| spelling | doaj.art-dd5792095f78461bbb633f895316e3e22022-12-22T03:45:02ZaraCollege of Education for Pure Sciencesمجلة التربية والعلم1812-125X2664-25302022-09-01313919810.33899/edusj.2022.134241.1251174956hα-Open Sets in Topological SpacesBaedaa Abdullah0Sabih Askandar1Ruqayah Balo2Mathematics Department/college of education for pure sciences/mosul universityMathematics/College of Education for Pure Science/Mosul Universitymathematics department/college of education for pure sciences/mosul universityIn 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.https://edusj.mosuljournals.com/article_174956_f40d28d40eb2b9d6731dba30a0e35796.pdfh∝-open set,,,،,؛h∝-continuous mapping,,,،,؛h∝-open mapping,,,،,؛h∝-totally continuous mapping,,,،,؛h∝-irresolute mapping |
| spellingShingle | Baedaa Abdullah Sabih Askandar Ruqayah Balo hα-Open Sets in Topological Spaces مجلة التربية والعلم h∝-open set,, ,،,؛h∝-continuous mapping,, ,،,؛h∝-open mapping,, ,،,؛h∝-totally continuous mapping,, ,،,؛h∝-irresolute mapping |
| title | hα-Open Sets in Topological Spaces |
| title_full | hα-Open Sets in Topological Spaces |
| title_fullStr | hα-Open Sets in Topological Spaces |
| title_full_unstemmed | hα-Open Sets in Topological Spaces |
| title_short | hα-Open Sets in Topological Spaces |
| title_sort | hα open sets in topological spaces |
| topic | h∝-open set,, ,،,؛h∝-continuous mapping,, ,،,؛h∝-open mapping,, ,،,؛h∝-totally continuous mapping,, ,،,؛h∝-irresolute mapping |
| url | https://edusj.mosuljournals.com/article_174956_f40d28d40eb2b9d6731dba30a0e35796.pdf |
| work_keys_str_mv | AT baedaaabdullah haopensetsintopologicalspaces AT sabihaskandar haopensetsintopologicalspaces AT ruqayahbalo haopensetsintopologicalspaces |