B-open Sets Research Articles

Ultrasoft B-Open Sets and Ultrasoft B-Continuous Functions

Ultrasoft B-Open Sets and Ultrasoft B-Continuous Functions

Enhancing decision-making in breast cancer diagnosis for women through the application of nano beta open sets

Nano topology is a modern type of topology based on rough sets, introducing nano open sets and their properties. This study explores the new properties of nano-β-open sets and nano-closures in nano topological space, providing some equivalent definitions, theorems, and lemmas for illustration. The effectiveness of incorporating nano β-open sets in medical decision-making is demonstrated in diagnosing breast cancer in two cases for women. Results indicated that utilizing nano open sets enhanced the accuracy, sensitivity, and specificity of cancer diagnosis. Additionally, an algorithm has been developed to aid clinicians in diagnosing breast cancer infections. The overarching objective is to provide physicians with a valuable tool to make informed decisions and reach optimal conclusions in patient care.

ON t^*-SET AND B^*-SET IN NANO TOPOLOGICAL SPACES

We investigate the class of nano locally **b-closed sets in this paper. The purpose of this work is to introduce several novel sets, such as nano closed sets,nano t*-sets, nano *b-closed sets, nano B*-set and nano **b-closed sets, and to investigate the properties of these sets. We also introduced the concept of nano **b-open sets and nano locally **b-open sets, as well as examined some of their features.

Hypersoft b-Open Sets and Hypersoft b-Continuous Function

Hypersoft b-Open Sets and Hypersoft b-Continuous Function

Soft G*β-Separation Axioms in Soft Topological Spaces

Soft set theory is a newly emerging tool to deal with uncertain problems and has been studied by researchers in theory and practice. The concept of soft topological space is a very recently developed area having many research scopes. Soft sets have been studied in proximity spaces, multicriteria decision-making problems, medical problems, mobile cloud computing networks, defense learning system, approximate reasoning etc. In 2020 Punitha Tharani and H. Sujitha introduced a new class of soft generalized star β-closed (Sft*β-closed) sets and Sft*β-open sets in soft topological spaces. They investigated some basic properties of Sft* β-closed sets and Sft*β-open sets. They also studied the relationship between this type of closed sets and other existing closed sets in soft topological spaces. The aim of this paper is to introduce some soft separation axioms called Sftg*β-R0 space, Sftg* β-R1 space, Sftg*β-T0 space, Sftg*β-T1 space, Sftg*β-T2 space, Sftg* β-regular space and Sftg*β-normal space in soft topological spaces. We investigate several properties and characterizations of this spaces in soft topological spaces.

Weakly soft b-open sets and their usages via soft topologies: A novel approach

The objective of the current article, is introducing the notion of weakly soft b-open subsets (ws b-open) and investigating some of its properties. A lot of relationships between this family of soft sets and some generalizations of soft open sets with some interpretative examples are examined. With extended and hyperconnected soft topologies, various relevant outcomes and several relationships are achieved. By ws b-open and weakly soft b-closed (ws b-closed) sets, the weakly b- interior, weakly b-closure operators are constructed and soft continuity are established with some of their substantial features. Commonly, the methodical relations and results that are lost through this study are discussed. The necessary stipulations to preserve some of these relations and results like extended, full, and hyperconnected soft topology are demonstrated.

On weakly soft β-open sets and weakly soft β-continuity

This work introduces weakly soft β-open subsets, a new family of soft-open sets. By this family, we expand a soft topology to a soft structure which is neither supra-soft topology nor infra-soft topology. The connections between this class of soft sets and other celebrated classes via soft topology are examined with some elucidative examples. Also, it is established some relationships under conditions of extended and hyperconnected soft topologies. Furthermore, the interior and closure operators are structured along with weakly soft β-open and weakly soft β-closed sets. Finally, the class of weakly soft β-continuous functions is introduced and its main characterizations are studied. It is investigated the systematic relationships and findings that are lost for this kind of soft continuity as well as it is shown the conditions required to maintain some of these relationships such as full, extended and hyperconnected soft topologies.

Covering Properties via Neutrosophic b-open Sets

The purpose of this article is to study some covering properties in neutrosophic topological spaces using neutrosophic b-open sets. We define neutrosophic b-open cover, neutrosophic b-compactness, neutrosophic countably b-compactness neutrosophic b-Lindelofness, neutrosophic local b-compactness and study various properties entangled with them. We study some covering properties involving neutrosophic continuous, neutrosophic b-continuous and neutrosophic b*-continuous functions. Lastly, we define neutrosophic base, neutrosophic subbase, neutrosophic second countability via neutrosophic b-open sets and investigate some properties.

$b^{\ast}_{I}$ Sets and $b^{\ast}_{I}$-Compact Ideal Spaces

We came up with the concept b∗-open set which has stricter condition with respect to the notion b-open sets, introduced by Andrijevic [2] as a generalization of Levine’s [7] generalized closed sets. The condition imposes equality instead of inclusion. In this study, we gave some important properties of b∗-open sets with respect to an ideal, and b∗-compact spaces.

Pairwise Neutrosophic Simply b-Open Set via Neutrosophic Bi-topological Spaces

In this article an attempt has been made to procure the concept of pairwise neutrosophic simply open set, pairwise neutrosophic simply continuous mapping, pairwise neutrosophic simply open mapping, pairwise neutrosophic simply compactness, pairwise neutrosophic simply b-open set, pairwise neutrosophic simply b-continuous mapping, pairwise neutrosophic simply b-open mapping and pairwise neutrosophic simply b-compactness via neutrosophic bi-topological spaces (in short NBTS). Besides, we furnish few illustrative examples on them via NBTS. Further, we investigate some basic properties of them, and formulate several results on NBTSs.

Neutrosophic grb-Continuous and grb-Irresolute Mappings in Neutrosophic Topological Spaces

Real-life structures always include indeterminacy. The Mathematical tool which is well known in dealing with indeterminacy is neutrosophic. Smarandache proposed the approach of neutrosophic sets. Neutrosophic sets deal with uncertain data. The notion of neutrosophic set is generally referred to as the generalization of intuitionistic fuzzy set. In 2021, Dr. G. Sindhu introduced the concept of Neutrosophic generalized regular b-closed sets and neutrosophic generalized b-open sets and presented some of their properties in Neutrosophic topological spaces. In this research paper, we introduce the concepts of neutrosophic grb-continuous mappings, neutrosophic grb-irresolute mappings, neutrosophic grb-closed mappings, neutrosophic grb-open mappings, strongly neutrosophic grb-continuous mappings, perfectly neutrosophic grb-continuousmappings, neutrosophic contra grb-continuous mappings and neutrosophic contra grb-irresolute mappings in neutrosophic topological spaces. We investigate and obtain several properties and characterizations concerning these mappings in neutrosophic topological spaces.

Sets And Functions In Terms Of Local Function

In this paper, a collection of sets are investigated in such a way that the collection splits in the collection of preopen sets and the collection of b-open sets and also splits in the collection of semi-open sets and the collection of b-open sets. Functions in terms of this sets is a part of this paper and it will be considered that these collection remains invariant under homeomorphic image.

Between the Classes of Soft Open Sets and Soft Omega Open Sets

In this paper, we define the class of soft ω0-open sets. We show that this class forms a soft topology that is strictly between the classes of soft open sets and soft ω-open sets, and we provide some sufficient conditions for the equality of the three classes. In addition, we show that soft closed soft ω-open sets are soft ω0-open sets in soft Lindelof soft topological spaces. Moreover, we study the correspondence between soft ω0-open sets in soft topological spaces and ω0-open sets in topological spaces. Furthermore, we investigate the relationships between the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of a given soft anti-locally countable soft topological space and the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of the soft topological space of soft ω0-open sets generated by it. Finally, we introduce ω0-regularity in topological spaces via ω0-open sets, which is strictly between regularity and ω-regularity, and we also introduce soft ω0-regularity in soft topological spaces via soft ω0-open sets, which is strictly between soft regularity and soft ω-regularity. We investigate relationships regarding ω0-regularity and soft ω0-regularity. Moreover, we study the correspondence between soft ω0-regularity in soft topological spaces and ω0-regularity in topological spaces.

Neutrosophic Soft Quad Structures Concerning Neutrosophic Soft Points

In this article, a new concept of neutrosophic soft quad-topological structures is introduced. Generalised neutrosophic soft ∗ b open sets in neutrosophic soft quad-topological structures concerning soft points of the space are introduced. Different results are addressed in neutrosophic soft quad-topological structure on the basis of these new neutrosophic soft ∗ b open sets. Neutrosophic soft separation axioms and other separation axioms are addressed in neutrosophic soft quad-topological structures. The engagement of these axioms is switched over with different results with respect to soft points. Neutrosophic soft topological properties of some results are also addressed in neutrosophic soft quad-topological structure. To secure the results, examples are constructed. The nonvalidity of some results are justified with examples. The understanding of some complicated problems is secured with simple techniques.

Nano Fuzzy b-open Sets in Nano fuzzy Topological Spaces

The purpose of this paper is to define and study a new class of Nano fuzzy open sets called Nano fuzzy b-open sets in Nano fuzzy topological spaces. We have tried to analyze the basic properties of Nano fuzzy b-open sets. We have also used these Nano fuzzy b-open sets to introduce a new type of Nano fuzzy continuous functions, which are called Nano fuzzy b-open continuous functions and their properties are investigated.

On *b-open sets and *b-open sets in nano topological spaces

On *b-open sets and *b-open sets in nano topological spaces

Neutrosophic Simply b-Open Set in Neutrosophic Topological Spaces

In this paper, we procure the notions of neutrosophic simply b-open set, neutrosophic simply b-open cover, and neutrosophic simply b-compactness via neutrosophic topological spaces. Then, we establish some remarks, propositions, and theorems on neutrosophic simply
 b-compactness. Further, we furnish some counter examples where the result fails.

A look at soft neutrosophic spaces

In this article, new definition of neutrosophic soft ** b-open set is introduced with the help of neutrosophic soft α-open set and neutrosophic soft β-open set. With the application of this new definition some neutrosophic soft separation axioms and neutrosophic soft other separation axioms are addressed with respect to soft points of the spaces. Suitable examples are provided for the clarification of different results. Soft countability results and its engagements with different other neutrosophic soft results are studied. In continuation, characterization of Bolzano Weirstrass Property with respect to neutrosophic soft results and neutrosophic soft compactness results are inaugurated.

Separation Axioms in Topological Ordered Spaces Via b-open Sets

This paper aims to define and study new separation axioms based on the b-open sets in topological ordered spaces, namely strong - -ordered spaces ( ). These new separation axioms are lying between strong -ordered spaces and - - spaces ( ). The implications of these new separation axioms among themselves and other existing types are studied, giving several examples and counterexamples. Also, several properties of these spaces are investigated; for example, we show that the property of strong - -ordered spaces ( ) is an inherited property under open subspaces.

A new decomposition of open and closed sets in topological spaces

In this paper, we show some properties on *b-open sets. Besides, we introduce the notions of generalized *b-closed sets, locally *b-closed sets, regular generalized *b-closed sets and weakly *b-closed sets. Moreover, we study some of their properties.