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 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 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 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 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 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 Note on the Union-Closed Sets Conjecture

10.37236/6989 ◽  
2017 ◽  
Vol 24 (3) ◽  
Author(s):  
Abigail Raz
Keyword(s):  
Finite Family ◽  
Closed Sets ◽  
Set Size ◽  
Do So

The union-closed sets conjecture states that if a finite family of sets $\mathcal{A} \neq \{\varnothing\}$ is union-closed, then there is an element which belongs to at least half the sets in $\mathcal{A}$. In 2001, D. Reimer showed that the average set size of a union-closed family, $\mathcal{A}$, is at least $\frac{1}{2} \log_2 |\mathcal{A}|$. In order to do so, he showed that all union-closed families satisfy a particular condition, which in turn implies the preceding bound. Here, answering a question raised in the context of T. Gowers' polymath project on the union-closed sets conjecture, we show that Reimer's condition alone is not enough to imply that there is an element in at least half the sets.

scholarly journals A Note on Some Generalized Closed Sets in Bitopological Spaces Associated to Digraphs

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
K. Kannan
Keyword(s):  
Graph Theory ◽  
Short Communication ◽  
Topological Spaces ◽  
Closed Sets ◽  
Bitopological Spaces ◽  
The Relationship

Many investigations are undergoing of the relationship between topological spaces and graph theory. The aim of this short communication is to study the nature and properties of some generalized closed sets in the bitopological spaces associated to the digraph. In particular, some relations between generalized closed sets in the bitopological spaces associated to the digraph are characterized.

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