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