Abstract
In this paper, we introduce and investigate some weak separation axioms by using the notions of \alpha-open sets and the \alpha -closure operator.
Highlights
Jafari abstract: In this paper, we introduce and investigate some weak separation axioms by using the notions of α-open sets and the α-closure operator
Definition 2 A topological space (X, τ ) is called α-D0 if for any distinct pair of points x and y of X there exists an αD-set of X containing x but not y or an αD-set of X containing y but not x
Definition 3 A topological space (X, τ ) is called α-D1 if for any distinct pair of points x and y of X there exists an αD-set of X containing x but not y and an αD-set of X containing y but not x
Summary
Definition 4 A topological space (X, τ ) is called α-D2 if for any distinct pair of points x and y of X there exists disjoint αD-sets G and E of X containing x and y, respectively. Definition 7 A subset A of a topological space (X, τ ) is called a (α, α)-generalizedclosed set [21] (briefly (α, α)-g-closed) if Clα(A) ⊂ U whenever A ⊂ U and U is α-open in (X, τ ).
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