Comment on Strongly Preirresolute Topological Vector Spaces

Authors : Madhu RAM, Sayed K ELAGAN

Pages : 229-231

Doi:10.31197/atnaa.831128

View : 16 | Download : 6

Publication Date : 2021-06-30

Article Type : Other Papers

Abstract :Let insert ignore into journalissuearticles values(X, =); be a topological space. A subset A of X is called pre-open if A ⊆ Intinsert ignore into journalissuearticles values(Clinsert ignore into journalissuearticles values(A););. Let P Oinsert ignore into journalissuearticles values(X); denote the family of all pre-open sets in X. In general, P Oinsert ignore into journalissuearticles values(X); does not form a topology on X. Furthermore, in topological vector spaces, it is not always true that P Oinsert ignore into journalissuearticles values(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 Oinsert ignore into journalissuearticles values(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