Comment on Strongly Preirresolute Topological Vector Spaces

Yıl 2021, Cilt: 5 Sayı: 2, 229 - 231, 30.06.2021

Madhu Ram Sayed K Elagan

https://doi.org/10.31197/atnaa.831128

Öz

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.

Anahtar Kelimeler

Pre-open sets, topological vector spaces, strongly preirresolute topological vector spaces

Kaynakça

• [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.