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Journals / Advances in the Theory of Nonlinear Analysis and its Application / 2026 / Cilt: 5 Sayı: 2

Comment on Strongly Preirresolute Topological Vector Spaces

Madhu Ram(University of Jammu)0000-0001-6583-0978
Sayed K Elagan(Taif university)
Pages
229–231
Publication Date
2021-06-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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 see that all proved results in [5] concerning strongly preirresolute topological vector spaces are obvious.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let (X, =) be a topological space.
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Key Findings & Data:A subset A of X is called pre-open if A ⊆ Int(Cl(A)).
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Conclusion & Impact: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 see that all proved results in [5] concerning strongly preirresolute topological vector spaces are obvious.
🔬Design:Not
📍Scope:Comprehensive Sample
⚙️Variables:Pre-open sets · topological vector spaces · strongly preirresolute topological vector spaces

Abstract

Let (X, =) be a topological space. A subset A of X is called pre-open if A ⊆ Int(Cl(A)). Let P O(X) denote the family of all pre-open sets in 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 where 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 see that all proved results in [5] concerning strongly preirresolute topological vector spaces are obvious.

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Cite This Article

Ram, M., Elagan, S. K. (2021). Comment on Strongly Preirresolute Topological Vector Spaces. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 5 Sayı: 2, 229–231. https://doi.org/10.31197/atnaa.831128

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References (7)

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