Results on a Pre-T_2 Space and Pre-Stability
This paper contains an equivalent statements of a pre- space, where are considered subsets of with the product topology. An equivalence relation between the preclosed set and a pre- space, and a relation between a pre- space and the preclosed set with some conditions on a function are found....
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| Format: | Article |
| Language: | Arabic |
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College of Science for Women, University of Baghdad
2019-03-01
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| Series: | Baghdad Science Journal |
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| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3177 |
| _version_ | 1828274482242912256 |
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| author | Anmar Hashim Jasim |
| author_facet | Anmar Hashim Jasim |
| author_sort | Anmar Hashim Jasim |
| collection | DOAJ |
| description | This paper contains an equivalent statements of a pre- space, where are considered subsets of with the product topology. An equivalence relation between the preclosed set and a pre- space, and a relation between a pre- space and the preclosed set with some conditions on a function are found. In addition, we have proved that the graph of is preclosed in if is a pre- space, where the equivalence relation on is open.
On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that a pre-stable ( pre-stable) set is positively invariant (invariant), and we add a condition on this set to prove the converse. Finally, a relationship between, (i) a pre-stable ( pre-stable) set and its component (ii) a pre- space and a (positively critical point) critical point, are gotten. |
| first_indexed | 2024-04-13T06:35:07Z |
| format | Article |
| id | doaj.art-eb062704e87c4da48ce0b7dd15d85cd1 |
| institution | Directory Open Access Journal |
| issn | 2078-8665 2411-7986 |
| language | Arabic |
| last_indexed | 2024-04-13T06:35:07Z |
| publishDate | 2019-03-01 |
| publisher | College of Science for Women, University of Baghdad |
| record_format | Article |
| series | Baghdad Science Journal |
| spelling | doaj.art-eb062704e87c4da48ce0b7dd15d85cd12022-12-22T02:57:56ZaraCollege of Science for Women, University of BaghdadBaghdad Science Journal2078-86652411-79862019-03-0116110.21123/bsj.16.1.01113177Results on a Pre-T_2 Space and Pre-StabilityAnmar Hashim JasimThis paper contains an equivalent statements of a pre- space, where are considered subsets of with the product topology. An equivalence relation between the preclosed set and a pre- space, and a relation between a pre- space and the preclosed set with some conditions on a function are found. In addition, we have proved that the graph of is preclosed in if is a pre- space, where the equivalence relation on is open. On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that a pre-stable ( pre-stable) set is positively invariant (invariant), and we add a condition on this set to prove the converse. Finally, a relationship between, (i) a pre-stable ( pre-stable) set and its component (ii) a pre- space and a (positively critical point) critical point, are gotten.http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3177A preirresolute function, A pre-stable (γpre-stable) set, Preopen, Positively invariant, Positively critical point |
| spellingShingle | Anmar Hashim Jasim Results on a Pre-T_2 Space and Pre-Stability Baghdad Science Journal A preirresolute function, A pre-stable (γpre-stable) set, Preopen, Positively invariant, Positively critical point |
| title | Results on a Pre-T_2 Space and Pre-Stability |
| title_full | Results on a Pre-T_2 Space and Pre-Stability |
| title_fullStr | Results on a Pre-T_2 Space and Pre-Stability |
| title_full_unstemmed | Results on a Pre-T_2 Space and Pre-Stability |
| title_short | Results on a Pre-T_2 Space and Pre-Stability |
| title_sort | results on a pre t 2 space and pre stability |
| topic | A preirresolute function, A pre-stable (γpre-stable) set, Preopen, Positively invariant, Positively critical point |
| url | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3177 |
| work_keys_str_mv | AT anmarhashimjasim resultsonapret2spaceandprestability |