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In this paper, we propose a unified concept encompassing generalizations of two types of families defined based on Levine's notions of generalized closed sets and Maki's  Λ  sets. The methods used in this investigation are described in my previous work, where a unified concept of general closedness is presented. From a methodology point of view, the present concept is symmetric to the previous. In generalizing open subsets, one can use the two methods. According to the first one, the family of Levine's generalization is used as some base to build the family of closed subsets of the new topology. In the second method, the family of open subsets is extended, in the same way, as the family of closed subsets in the classic Levine's method. The results obtained in this general conception easily extend and imply well-known theorems of this area of investigation. In the literature on this issue, many versions of generalizations of  Λ -sets have been investigated. The tools used in this paper enabled us to prove that there exist at most 10 generalizations of these types, and we show the relationships between them in the graph. As a result, it turns out that some generalizations investigated in the literature are trivial. [ABSTRACT FROM AUTHOR]

The concept of relative topological properties was introduced by Arhangel'skii and Gennedi and was subsequently investigated by many authors for different notions of general topology. In this paper few semi-separation axioms in relative sense are introduced and studied by utilizing semi-open sets. Characterizations and preservation under mapping of these newly defined notions are provided. Relationship that exists between these notions, with some of the absolute properties and with the existing relative separation axioms are investigated. [ABSTRACT FROM AUTHOR]

An S-Topological BE-Algebras(STBE-Algebras) is a BE-Algebra equipped with a special type of topology that makes the operation (defined on it)as S-topological continuous. In this paper, we discuss the separation axioms on a STBE-Algebras. [ABSTRACT FROM AUTHOR]

The question as to the number of sets obtainable from a given subset of a topological space using the operators derived by composing members of the set {b, i, ∨, ∧}, where b, i, ∨ and ∧ denote the closure operator, the interior operator, the binary operators corresponding to union and intersection, respectively, is called the Kuratowski {b, i, ∨, ∧}-problem. This problem has been solved independently by Sherman [21] and, Gardner and Jackson [13], where the resulting 34 plus identity operators were depicted in the Hasse diagram. In this paper we investigate the sets of fixed points of these operators. We show that there are at most 23 such families of subsets. Twelve of them are the topology, the family of all closed subsets plus, well known generalizations of open sets, plus the families of their complements. Each of the other 11 families forms a complete complemented lattice under the operations of join, meet and negation defined according to a uniform procedure. Two of them are the well known Boolean algebras formed by the regular open sets and regular closed sets, any of the others in general need not be a Boolean algebras. [ABSTRACT FROM AUTHOR]

We define and study strong SH-open sets, SH-sets and Sβ-H-sets. [ABSTRACT FROM AUTHOR]

The definition of the product of topologies is generalized in such a way that topologies are replaced by generalized topologies in the sense of [3]. [ABSTRACT FROM AUTHOR]

Several concepts generalizing the notion of connectedness of a topological space are investigated. It is obtained that some of these concepts are equivalent (without or with additional conditions). [ABSTRACT FROM AUTHOR]

In the paper [5], several operations on generalized topologies are considered. They are not monotone in general, but an old result on monotonicity may be sharpened. [ABSTRACT FROM AUTHOR]