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Cited by 2 publications
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We define -closure operator as a new topological operator which lies between the -closure and the -closure. Some relationships between this new operator and each of -closure, -closure, and usual closure are obtained. Via -closure operator, we introduce -open sets as a new topology. Some mapping theorems related to the new topology are given. 2 topological spaces are characterized in terms of -closure operator. Also, we use -open sets to define -regularity as a new separation axiom which lies strictly between -regularity and regularity. For a given topological space ( , ), we show that -regularity is equivalent to the condition = . Finally, -continuity, --continuity, weak -continuity, and faint -continuity are introduced and studied. Definition 2.1.[1] Let be a subset of a ts ( , ).a. The -closure of is denoted by ( ) and defined by
We define -closure operator as a new topological operator which lies between the -closure and the -closure. Some relationships between this new operator and each of -closure, -closure, and usual closure are obtained. Via -closure operator, we introduce -open sets as a new topology. Some mapping theorems related to the new topology are given. 2 topological spaces are characterized in terms of -closure operator. Also, we use -open sets to define -regularity as a new separation axiom which lies strictly between -regularity and regularity. For a given topological space ( , ), we show that -regularity is equivalent to the condition = . Finally, -continuity, --continuity, weak -continuity, and faint -continuity are introduced and studied. Definition 2.1.[1] Let be a subset of a ts ( , ).a. The -closure of is denoted by ( ) and defined by
We introduce and investigate the concepts of θ ω -limit points and θ ω -interior points, and we use them to introduce two new topological operators. For a subset B of a topological space Y , σ , denote the set of all limit points of B (resp. θ -limit points of B , θ ω -limit points of B , interior points of B , θ -interior points of B , and θ ω -interior points of B ) by D B (resp. D θ B , D θ ω B , Int B , Int θ B , and Int θ ω B ). Several results regarding the two new topological operators are given. In particular, we show that D θ ω B lies strictly between D B and D θ B and Int θ ω B lies strictly between Int θ B and Int B . We show that D B = D θ ω B (resp. Cl θ B = Cl θ ω B and D B = D θ ω B = D θ B ) for locally countable topological spaces (resp. antilocally countable topological spaces and regular topological spaces). In addition to these, we introduce several product theorems concerning metacompactness.
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