scholarly journals Some Games with Soft -ᶅ-Pre-Generalized Open Sets

2021 ◽  
Vol 34 (4) ◽  
pp. 45-57
Author(s):  
Hammood A. A ◽  
Esmaeel R. B
Keyword(s):  
Separation Axiom ◽  
Closed Sets ◽  
Closed Groups ◽  
The Relationship

    In this paper, the concept of soft closed groups is presented using the soft ideal pre-generalized open and soft pre-open, which are -ᶅ- - -closed sets " -closed", Which illustrating several characteristics of these groups.  We also use some games and   -  Separation Axiom, such as (Æ®0, Ó¼, ᶅ) that use many tables and charts to illustrate this. Also, we put some proposals to study the relationship between these games and give some examples.

scholarly journals On Kuratowski I-convergence of sequences of closed sets

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 899-912
Author(s):  
Özer Talo ◽  
Yurdal Sever
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Closed Sets ◽  
Convergence Of Sequences ◽  
Positive Integers ◽  
The Relationship ◽  
Convergent Sequences

In this paper we extend the concepts of statistical inner and outer limits (as introduced by Talo, Sever and Ba?ar) to I-inner and I-outer limits and give some I-analogue of properties of statistical inner and outer limits for sequences of closed sets in metric spaces, where I is an ideal of subsets of the set N of positive integers. We extend the concept of Kuratowski statistical convergence to Kuratowski I-convergence for a sequence of closed sets and get some properties for Kuratowski I-convergent sequences. Also, we examine the relationship between Kuratowski I-convergence and Hausdorff I-convergence.

scholarly journals The Relationship of the Natural and the Social in Intragroup and Intergroup Relations in a Situation of Interethnic Conflicts

2021 ◽  
Vol 16 (5) ◽  
pp. 87-98
Author(s):  
Subbotina Nadezhda D. ◽  
Keyword(s):  
Intergroup Relations ◽  
Ethnic Relations ◽  
Point Of View ◽  
Main Task ◽  
Natural Group ◽  
Group Relations ◽  
The Social ◽  
The Hierarchical Structure ◽  
Closed Groups ◽  
The Relationship

The problem of interethnic conflicts is currently one of the topics attracting the attention of researchers of various specialties – culturologists, anthropologists, historians, social psychologists and others. The purpose and main task of this study is to analyze from a philosophical point of view the dialectics of the natural and the social in ethnic relations and its manifestation in interethnic conflicts. Accordingly, the article uses dialectical and comparative approaches. The theoretical basis of the study is the author’s concept of the relationship between natural and social in society and a man, which made it possible to identify the structure of ethnic relations according to this criterion, to determine the differences between social-group and natural-group relations. Intragroup and intergroup relations, in which natural components prevail over social ones are designated by the concept of “natural-group relations” (NGR) introduced in the author’s methodology. The specific results of the research and the novelty are the discovery of the specificity of the manifestation of the patterns of natural group relations and the role of suggestion in interethnic conflicts. It is proved that the concept of “group centrism” is not enough for the analysis of groups, since it describes mainly the assessment of one’s group and its values, and the concept of “regularities of natural group relations” denotes the hierarchical structure of a group, mechanisms of forced identification (including by methods of education) and self-identification, intragroup and intergroup relationships, reasons for conformism, etc. The article proves that the symptoms of grouping thinking, which were identified by I. L. Janis in small closed groups, and which are a kind of (NGR) patterns, are manifested with some variations in large groups. It is concluded that authors studying group relations do not pay enough attention to the natural prerequisites for the formation of groups and grouping of thinking, the fact that, due to the need for survival, the desire to unite into groups, to form and protect the uniformity of thinking is inherent in our genetic programs and is supported by suggestion. he further part of the article is devoted to the analysis of two interethnic conflicts based on the developed methodology ‒ the Arab-Israeli and Uzbek-Kyrgyz and the forecast, as well as the possibility of overcoming them.

scholarly journals Remarks on soft omega-closed sets in soft topological spaces

2014 ◽  
Vol 33 (1) ◽  
pp. 181
Author(s):  
Nirmala Rebecca Paul
Keyword(s):  
Compact Space ◽  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
The Relationship

The paper introduces soft omega-closed sets in soft topological spaces and establishes the relationship between other existing generlised closed sets in soft topological spaces. It derives the basic properties of soft omega-closed sets. As an application it proves that a soft omega-closed set in a soft compact space is soft compact.

scholarly journals Well-Graded Families and the Union-Closed Sets Conjecture

10.37236/8380 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Jeffrey Matayoshi
Keyword(s):  
Finite Family ◽  
Closed Sets ◽  
The Relationship ◽  
Extra Structure

The union-closed sets conjecture states that if a finite family of sets $\mathcal{F}$ is union-closed, then there must be some element contained in at least half of the sets of $\mathcal{F}$.  In this work we study the relationship between the union-closed sets conjecture and union-closed families that have the property of being well-graded.  In doing so, we show how the density and other properties are affected by the extra structure contained in well-graded families, and we also give several conditions under which well-graded families satisfy the union-closed sets conjecture.

scholarly journals Neutrosophic Ideal layers Some Generalizations for GIS Topological Rules

2020 ◽  
pp. 44-49
Author(s):  
A. A. Salama ◽  
◽  
◽  
Rafif Alhabib
Keyword(s):  
Information Systems ◽  
Geographical Information Systems ◽  
Geographical Information ◽  
Closed Sets ◽  
The Relationship

This paper aims to introduce and study some new neutrosophic fuzzy pairwise notions via neutrosophic fuzzy ideals. We, also generalize the notion of FPL-open sets. In addition to generalizing the concept of FPL-closed sets and NPL-open function, the relationship between the above new neutrosophic Fuzzy pairwise notions and there other relevant classes are investigated. In Geographical information systems (GIS) there is a need to statistically model spatial regions with indeterminate boundary and under indeterminacy. Possible applications to GIS rules are touched upon.

On statistical convergence of sequences of closed sets in metric spaces

2021 ◽  
Vol 71 (2) ◽  
pp. 409-422
Author(s):  
Dimitrios Georgiou ◽  
Athanasios Megaritis ◽  
Georgios Prinos ◽  
Fotini Sereti
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Closed Sets ◽  
Convergence Of Sequences ◽  
The Relationship

Abstract In this paper, we do further investigations on the statistical inner and outer limits of sequences of closed sets in metric spaces, which were introduced by Nuray, Rhoades, and Talo, Sever, Başar, and generalize the conventional Painleve-Kuratowski inner and outer limits. Also, we provide criteria for checking statistical Wijsman and Hausdorff set convergences and we examine the relationship between Kuratowski and Wijsman statistical convergence. A closer look on the concept of statistical Cauchyness, with respect to the Hausdorff “extended” metric h, completes this research.

scholarly journals On statistically convergent sequences of closed sets

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1497-1509 ◽  
Author(s):  
Özer Talo ◽  
Yurdal Sever ◽  
Feyzi Başarc
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Closed Sets ◽  
The Relationship ◽  
Convergent Sequences

In this paper, we give the definitions of statistical inner and outer limits for sequences of closed sets in metric spaces. We investigate some properties of statistical inner and outer limits. For sequences of closed sets if its statistical outer and statistical inner limits coincide, we say that the sequence is Kuratowski statistically convergent. We prove some proporties for Kuratowski statistically convergent sequences. Also, we examine the relationship between Kuratowski statistical convergence and Hausdorff statistical convergence.

scholarly journals Certain Types of Continuity via Ig**α-Closed Sets

2017 ◽  
Vol 19 ◽  
pp. 20-29
Author(s):  
C. Santhini ◽  
M. Suganya
Keyword(s):  
Continuous Functions ◽  
Closed Sets ◽  
The Relationship

In this paper we introduce and investigate the notion of Ig**α-continuous functions, almost Ig**α-continuous functions and discussed the relationship withother continuous functions and obtained their characteristics. Finally we obtain the decomposition of *α-continuity.

scholarly journals Binary Regular ^ Generalized Closed Sets In Binary Topological Spaces

2019 ◽  
pp. 279-282
Author(s):  
D. Savithiri ◽  
C. Janaki
Keyword(s):  
Topological Spaces ◽  
Closed Sets ◽  
The Relationship

In this article, we introduce binary regular ^ generalized closed sets <strong>(shortly µ<sub>b</sub> r^g-closed sets) </strong>in binary topological spaces. Also we examine some of its properties. Furthermore we study the relationship between these binary r^g-closed sets with other binary closed sets in binary topological spaces.

scholarly journals New Separation Axiom on ^-closed sets.

2012 ◽  
Vol 59 (3) ◽  
pp. 1-5
Author(s):  
M. LellisThivagar ◽  
M. Anbuchelvi
Keyword(s):  
Separation Axiom ◽  
Closed Sets
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