Comment on Strongly Preirresolute Topological Vector Spaces

Open Access

Original research article

Author(s):

Madhu Ram^a, Sayed K. Elagan^b

^aDepartment of Mathematics, University of Jammu, Jammu–180006, J&K, India.
^bDepartment of Mathematics and Statistics, Faculty of Science, P.O. 888, Taif University, Saudi Arabia.

Advances in the Theory of Nonlinear Analysis and its Applications 5(2), 229-231.

Received: November 25, 2020

Accepted: March 8, 2021

Published: April 4, 2021

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, strongly preirresolute topological vector spaces.

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APA Style

Ram, M., & Elagan, S. K. (2021). Comment on strongly preirresolute topological vector spaces. Advances in the Theory of Nonlinear Analysis and its Application, 5(2), 229-231.