Comment on Strongly Preirresolute Topological Vector Spaces

Year 2021, Volume: 5 Issue: 2, 229 - 231, 30.06.2021

Madhu Ram Sayed K Elagan

https://doi.org/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.

Keywords

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

References

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