Comment on strongly preirresolute topological vector spaces
A subset A of a topological space X is said to be pre-open if A ⊆ Int(Cl(A)). Let P O(X) denote the family of all pre-open sets in a given topological space X. In general, P O(X) does not form a topology on X. Furthermore, in topological vector spaces, it is not always true that P O(L) forms a top...
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| Format: | Article |
| Language: | English |
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ATNAA
2021-04-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1414566 |
| _version_ | 1797912972227510272 |
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| author | Madhu Ram Sayed K Elagan |
| author_facet | Madhu Ram Sayed K Elagan |
| author_sort | Madhu Ram |
| collection | DOAJ |
| description | A subset A of a topological space X is said to be pre-open if A ⊆ Int(Cl(A)). Let P O(X) denote the family
of all pre-open sets in a given topological space X. In general, P O(X) does not form a topology on X.
Furthermore, in topological vector spaces, it is not always true that P O(L) forms a topology on L when L is
a topological vector space. In this note, we prove that the class of strongly preirresolute topological vector
spaces is that subclass of topological vector spaces in which P O(L) forms a topology and thereby we will
observe that all results which are proven in [5] concerning strongly preirresolute topological vector spaces
are obvious. |
| first_indexed | 2024-04-10T12:04:17Z |
| format | Article |
| id | doaj.art-1870b6c5f3974801b10b1a0822a3e027 |
| institution | Directory Open Access Journal |
| issn | 2587-2648 |
| language | English |
| last_indexed | 2024-04-10T12:04:17Z |
| publishDate | 2021-04-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-1870b6c5f3974801b10b1a0822a3e0272023-02-15T16:16:19ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482021-04-015222923110.31197/atnaa.831128Comment on strongly preirresolute topological vector spacesMadhu RamSayed K ElaganA subset A of a topological space X is said to be pre-open if A ⊆ Int(Cl(A)). Let P O(X) denote the family of all pre-open sets in a given topological space X. In general, P O(X) does not form a topology on X. Furthermore, in topological vector spaces, it is not always true that P O(L) forms a topology on L when L is a topological vector space. In this note, we prove that the class of strongly preirresolute topological vector spaces is that subclass of topological vector spaces in which P O(L) forms a topology and thereby we will observe that all results which are proven in [5] concerning strongly preirresolute topological vector spaces are obvious.https://dergipark.org.tr/tr/download/article-file/1414566pre-open setsstrongly preirresolute topological vector spaces |
| spellingShingle | Madhu Ram Sayed K Elagan Comment on strongly preirresolute topological vector spaces Advances in the Theory of Nonlinear Analysis and its Applications pre-open sets strongly preirresolute topological vector spaces |
| title | Comment on strongly preirresolute topological vector spaces |
| title_full | Comment on strongly preirresolute topological vector spaces |
| title_fullStr | Comment on strongly preirresolute topological vector spaces |
| title_full_unstemmed | Comment on strongly preirresolute topological vector spaces |
| title_short | Comment on strongly preirresolute topological vector spaces |
| title_sort | comment on strongly preirresolute topological vector spaces |
| topic | pre-open sets strongly preirresolute topological vector spaces |
| url | https://dergipark.org.tr/tr/download/article-file/1414566 |
| work_keys_str_mv | AT madhuram commentonstronglypreirresolutetopologicalvectorspaces AT sayedkelagan commentonstronglypreirresolutetopologicalvectorspaces |