- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 5 Issue: 2
- Comment on Strongly Preirresolute Topological Vector Spaces
Comment on Strongly Preirresolute Topological Vector Spaces
Authors : Madhu Ram, Sayed K Elagan
Pages : 229-231
Doi:10.31197/atnaa.831128
View : 4 | Download : 2
Publication Date : 2021-06-30
Article Type : Other
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.Keywords : Pre-open sets, topological vector spaces, strongly preirresolute topological vector spaces