Sobriety Via θ-Open Sets

On Weakly e*-θ-open Functions and Their Characterizations

“…e * θ -regular spaces which is a generalization of regular spaces and e * θ -normal spaces which has defined by Ayhan and Özkoc ¸ [3] as a generalization of regular spaces has defined via e * -θ -open sets [10]. In recent years, many authors have studied several forms of regularity; such as β θ -regularity [5], semiregularity [13], preregularity [9], b-regularity [20], e-regularity [18], β -regularity [17] and normality; such as β θ -normality [5], seminormality [14], prenormality [21], e-normality [8], e * -normality [8], e * θ -normality [3].…”

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The purpose of this study is to introduce a new class of regular spaces called e * θ -regular spaces which is a generalization of the class of β θ -regular spaces [5]. Also, we investigate some basic properties and several characterizations of e * θregular and e * θ -normal [3] spaces.

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Ideals on Generalized Topological Spaces

“…In 1980, Jankovic [12] proved that a space is Hausdorff if and only if every compact set is θ-closed. Recent applications of θ-open sets can be found in the paper of Caldas, Jafari and Latif [6], and in the paper of Cammaroto, Catalioto, Pansera and Tsaban [7].…”

The topology of θω-open sets

“…It is known that τ θ forms a topology on X coarser than the topology τ and τ θ = τ if and only if (X, τ) is regular. Authors in [6,7,17,18,[21][22][23][24][25]28] continued the study of θ-closure operator, θ-open sets, and their related topological concepts. Recently, authors in [8][9][10]19] have studied several generalizations of θ-open sets.…”