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Dergiler / 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)
Sayfa
229–231
Yayın Tarihi
2021-06-30
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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 Maddede Bu Makale

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Amaç & Hipotez:Let (X, =) be a topological space.
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Temel Bulgular & Veri:A subset A of X is called pre-open if A ⊆ Int(Cl(A)).
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Sonuç & Katkı: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.
🔬Tür:Not
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (7)

  1. P. Bandyopadhyay, Topological Vector Spaces, Lecture Notes.
  2. M. Infusino, Topological Vector Spaces, Monograph, University of Konstanz, 2015.
  3. A. Kar and P. Bhattacharyya, Some weak separation axioms, Bull. Calcutta Math. Soc., 82 (1990), 415-422.
  4. A.S. Mashhour, M.E. Abd El-Monsef, I.A. Hasanein and T. Noiri, Strongly compact spaces, Delta J. Sci., 8 (1984), 30-46.
  5. N. Rajesh and V. Vijayabharathi, On strongly preirresolute topological vector spaces, Mathematica Bohemica, 38 (1) (2013), 37-42.
  6. W. Rudin, Functional Analysis, McGraw-Hill, 2nd edition, 1991.
  7. H.H. Schaefer, Topological Vector Spaces, Springer-Verlag New York, 1971.