Open AccessSelective separability in (a)topological spaces
Author(s) -
Sheetal Luthra,
Harsh V. S. Chauhan,
B. K. Tyagi
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2111745l
Subject(s) - closure (psychology) , mathematics , separable space , topological space , counterexample , pure mathematics , topology (electrical circuits) , topological tensor product , discrete mathematics , combinatorics , mathematical analysis , functional analysis , biochemistry , chemistry , economics , market economy , gene
In this paper, we study selective versions of separability in (a)topological spaces with the help of some strong and weak forms of open sets. For this we use the notions of semi-closure, pre-closure, ?-closure, ?-closure and ?-closure and their respective density in (a)topological spaces. The interrelationships between different types of selective versions of separability in (a)topological spaces have been given by suitable counterexamples. Sufficient conditions are given for (a)topological spaces to be (a)Rt-separable and (a)Mt-separable for each t ? {s, p, ?, ?, ?}. It is shown that under some condition (a)Mt-separability and (a)Rt-separability are equivalent.