Some properties of S(n)-θ-closed spaces

Some properties of minimal S(α) and S(α)FC spaces

“…Let X be minimal S(n)-space and A ⊆ X. Then X is an S(n)-closed space (Corollary 2.3. in [7]) and A (weakly)…”

“…Dikranjan and Giuli [3] introduced a notion of the θ n -closure operator and developed a theory of S(n)-closed and S(n)-θ-closed spaces. Jiang, Reilly, and Wang [7] used the θ n -closure in studying properties of minimal S(n)-spaces.…”

“…In this paper we continue the investigation of S(n)-closed, S(n)θ-closed, minimal S(n) spaces with the use of θ(n)-complete accumulation points. As we introduce new classes of S(n)-spaces -S(n)-functionally compact spaces and to answer some questions raised in [3,7].…”

On the cardinality of S(n)-Spaces

“…In 1966 Velichko [29] introduced the notion of θ-closedness. For a subset M of a topological space X the θ-closure is defined by cl θ M = {x ∈ X : every closed neighborhood of x meets M}, M is θ-closed if cl θ M = M. This concept was used by many authors for the study of Hausdorff nonregular spaces [9,11,13,14,27,28] and [16][17][18][19][20][21][22][23]. The S(n)-spaces were introduced by Viglino in 1969 (see [30]) under the name T n -spaces.…”