Comment on Strongly Preirresolute Topological Vector Spaces

Madhu Ram,Sayed K Elagan

doi:10.31197/atnaa.831128

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.

Highlights

Introduction and the main resultLet (X, ) be a topological space
Consider a topological vector space L = R, where R is endowed with the standard topology
A function f : X → Y is called p−continuous if the inverse image of any pre-open subset of Y is open in X

Summary

Introduction

Let (X, ) (or X) be a topological space. A subset A ⊆ X is called pre-open if A ⊆ Int(Cl(A)). Let P O(X) denote the collection of all pre-open subsets of X. Are pre-open subsets of but A ∩ B

Results

Conclusion