Semi-open Sets Research Articles

A note on semi-open sets in triclosure spaces

In this paper, we used the notion of triclosure spaces to introduce and study the concept of semi-open set in triclosure spaces. Besides, we show some of their properties. Moreover, the notions of semi-continuous and semi-irresolute functions in a triclosure spaces are studied. Furthermore, we prove some of their properties.

On <i>M</i>-Asymmetric Semi-Open Sets and Semicontinuous Multifunctions in Bitopological Spaces

The purpose of this paper is to introduce the notions of m-asymmetric semiopen sets and M-asymmetric semicontinuous multifunctions defined between asymmetric sets satisfying certain minimal conditions in the framework of bitopological spaces. Some new characterizations of m-asymmetric semiopen sets and M-asymmetric semicontinuous multifunctions will be investigated and several fundamental properties will be obtained.

A note on semi-open sets in triclosure spaces

In this paper, we used the notion of triclosure spaces to introduce and study the concept of semi-open set in triclosure spaces. Besides, we show some of their properties. Moreover, the notions of semi-continuous and semi-irresolute functions in a triclosure spaces are studied. Furthermore, we prove some of their properties.

On psi _{{mathcal{H}}}( . )-operator in weak structure spaces with hereditary classes

Weak structure space (briefly, wss) has master looks, when the whole space is not open, and these classes of subsets are not closed under arbitrary unions and finite intersections, which classify it from typical topology. Our main target of this article is to introduce psi _{{mathcal {H}}}(.)-operator in hereditary class weak structure space (briefly, {mathcal {H}}wss) (X, w, {mathcal {H}}) and examine a number of its characteristics. Additionally, we clarify some relations that are credible in topological spaces but cannot be realized in generalized ones. As a generalization of w-open sets and w-semiopen sets, certain new kind of sets in a weak structure space via psi _{{mathcal {H}}}(.)-operator called psi _{{mathcal {H}}}-semiopen sets are introduced. We prove that the family of psi _{{mathcal {H}}}-semiopen sets composes a supra-topology on X. In view of hereditary class {mathcal {H}}_{0}, w T_{1}-axiom is formulated and also some of their features are investigated.

New Games via soft-I-Semi-g-Separation axioms

In this article, the notions are introduced by using soft ideal and soft semi-open sets, which are - - - -closed sets " -closed" where many of the properties of these sets are clarified. Some games by using soft- -semi, soft separation axioms: like ( 0 ( 0 Using many figures and proposition to study the relationships among these kinds of games with some examples are explained.

Limit Points and Separation Axioms with Respect to Supra Semi-open Sets

Sometimes we need to minimize the conditions of topology for different reasons such as obtaining more convenient structures to describe some real-life problems, or constructing some counterexamples whom show the interrelations between certain topological concepts, or preserving some properties under fewer conditions of those on topology. To contribute this research area, in this paper, we establish some new concepts on supra topological spaces using supra semi-open sets and give some characterizations of them. First, we introduce a concept of supra semi limit points of a set and study main properties, in particular, on the spaces that possess the difference property. Second, we define and investigate new separation axioms, namely supra semi Ti-spaces (i = 0, 1, 2, 3, 4) and give complete descriptions for each one of them. We provide some examples to show the relationships between them as well as with STi-space.

On Nano soft-ℐ-semi-g-closed sets

In this paper, the notions of nano soft closed sets were introduced by using nanosoft ideal and nano soft semi-open sets, which are nano soft-ℐ-semi-g-closed sets “n-sℐsgclosed” where many of the properties of these sets were clarified. Using many figures and proposition have been studied the relationships among these kinds of nano soft sets with some examples were explained.

On Separation Axioms With Soft-J-Semi-g-Open Sets

In this article, the notions of soft closed sets were introduced by using soft ideal and soft semi-open sets, which are soft-J-semi-g-closed sets "sJsg-closed" where many of the properties of these sets were clarified. Some definitions of near open soft functions, near and near soft continuous functions were offered like; soft Jsg-open functions, soft J *sg-open functions, soft J **sg-open functions, soft Jsg-continuous functions, strongly soft Jsg-continuous functions and soft Jsg-irresolute-functions. Some kinds of separation axioms and convergence in sequences were studied by using soft-J-semi-g-open sets like; sJsg-T 0space, sJsg-T 1-space, sJsg-T 2-space.Many figures and propositions have been studied the relationships among these kinds of near soft functions with some examples were explained.

More On Weak Soft Axioms

Abstract In this paper, we continue studying the properties of weak soft axioms discussed and studied in [8]. We initiate and explore soft semi-R 0 spaces at soft point in terms of soft semi-open sets and study its characterizations and properties. It is interesting to mention that this soft contains the soft semi-closure of each of its soft point singletons. We also define soft semi-R 1 spaces at soft point and discuss some of its characterizations.

Covering properties defined by preopen sets

In this paper, we study some covering properties in topological spaces defined by preopen sets. We introduce and investigate the properties of the pre-Menger property, the almost pre-Menger property and their star versions. It is shown that the pre-Menger and the semi-Menger [Covering properties defined by semi-open sets, J. Nonlinear Sci. Appl. 9 (2016) 4388–4398] are independent properties.

Properties of neutrosophic nano semi open sets

Properties of neutrosophic nano semi open sets

Neutrosophic Crisp Semi Separation Axioms In Neutrosophic Crisp Topological Spaces

The main goal of this paper is to propose a new type of separation axioms via neutrosophic crisp semi open sets and neutrosophic crisp points in neutrosophic crisp topological spaces, namely neutrosophic crisp semi separation axioms. Finally, we examine the relationship between them in details. And also includes the study of the connections between these neutrosophic crisp semi separation axioms and the existing neutrosophic crisp separation axioms. Moreover, many examples are presented, to illustrate the concepts introduced in this paper. and investigate their fundamental properties, relationships and characterizations.

Applications of fuzzy bitopological semi-open sets

Applications of fuzzy bitopological semi-open sets

On semi-open sets and Feebly open sets in generalized topological spaces

In this paper, we introduce the notion of semi-open sets and feebly open sets in generalized topological spaces. Several properties of these notions are discussed. Also this paper considers (semi and feebly)-separation axioms for generalized topological spaces. We further investigate (semi-continuous, feebly-continuous, almost open)-functions in generalized topological spaces.

Seven generalized types of soft semi-compact spaces

The soft compactness notion via soft topological spaces was first studied in [10,29]. In this work, soft semi-open sets are utilized to initiate seven new kinds of generalized soft semi-compactness, namely soft semi-Lindel\{o}fness, almost (approximately, mildly) soft semi-compactness and almost (approximately, mildly) soft semi- Lindel\{o}fness. The relationships among them are shown with the help of illustrative examples and the equivalent conditions of each one of them are investigated. Also, the behavior of these spaces under soft semi-irresolute maps are investigated. Furthermore, the enough conditions for the equivalence among the four sorts of soft semi-compact spaces and for the equivalence among the four sorts of soft semi-Lindel\{o}f spaces are explored. The relationships between enriched soft topological spaces and the initiated spaces are discussed in different cases. Finally, some properties which connect some of these spaces with some soft topological notions such as soft semi-connectedness, soft semi $T_2$-spaces and soft subspaces are obtained.

English

English

Soft Semi Local Functions in Soft Ideal Topological Spaces

In this paper, we define a soft semi local function (F, E) ∗s ( ˜I, τ ) by using semi open soft sets in a soft ideal topological space (X, τ, E, ˜I). This concept is discussed with a view to find new soft topologies from the original one, called ∗s-soft topology. Some properties and characterizations of soft semi local function are explored. Finally, the notion of soft semi compatibility of soft ideals with soft topologies is introduced and some equivalent conditions concerning this topic are established here.

Separating sets by bilaterally quasi-continuous functions

In this paper we characterize the pairs (A 0, A 1) and (A−, A +) of disjoint sets which can be separated by a bilaterally quasi-continuous function. Moreover, we characterize when two arbitrary subsets of the real line can be separated by bilaterally dense in themselves semi-open sets.

Semi compactness in fuzzifying bitopological spaces

In this paper, we dene semi open sets in the subspaces of fuzzifying bitopological spaces and study some properties of these sets. We introduce and study the concepts of semi-compactness in fuzzifying bitopological spaces. Also we give some properties of the semi-compactness in fuzzifying bitopological spaces.

I-Open Sets and Separating Axioms Spaces

The purpose of this paper is using a class of open sets called i-open sets [9] to study some classes of separating axioms spaces for open,  -open and semi-open sets. Further, we studied the relations between such spaces.